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GMAT PREP2 DS V2.0 (Share Prep数学 with U)


Share Prep 数学 with U Prep2 DS V2.0
(新增目录、超链接)

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众所周知,数学在 GMAT 考试中占据着举足轻重的地位,数学 的分数为 GMAT 之战必争之地。但是,由于数学是中国学生的强项, 所以市面上关于数学的复习资料又远没有语法、 逻辑、 阅读那样完备。 在与众多战友沟通的过程中,我们发现大家对于 prep 数学有较高的 依赖度,但市面上现存的 prep 数学讲解却不够完备与准确。于是, 版主们决定撰写 SharewithU prep 数学宝典, 对现有 prep 数学讲解进 行三个完善 —— 1、题库的完善。原有的 prep 数学讲解包含了 prep 软件中的 600 余道题,而本宝典新增题目 100 余道,为史上最完备! 2、讲解的完善。原有的 prep 数学讲解没有统一的格式,讲解想 到哪里讲到哪里,而本宝典中,每一道题目按照统一的解题思路进行 分析( DS 部分尤为明显) ,能够帮助大家更好地理清思路。 3、呈现形式的完善。原有的 prep 数学没有统一的呈现形式,而 本宝典中,每一题的讲解包括题目翻译、思路点拨、题目全解、难度 评级等部分,让大家可以对每一道题目有更为深刻的理解。 在这里,让我们衷心地感谢在申请、工作、学习繁忙之余拨冗点 评的每一位热心网友与版主:哒不溜、当不了和尚、dennissinned 、 lawcici、nancyklauberg、 rongyang114、sudagrape 、天才狮子、听暖、 欣欣向荣(按音序排列) ,没有他们的辛勤付出,就没有今天大家看 到的 SharewithU prep 数学宝典。

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当然,由于作者与编者的能力与精力有限,疏漏之处在所难免, 如有发现错误之处,欢迎大家跟贴指正! 附件中,题号用黄色标注的部分题目因题目不完整而无法分析, 如有大家有其中某一题或几题的完整版题目,欢迎大家跟贴补充! 大家每一次的讨论,每一次的纠正,每一次的补充,都会成为 SharewithU prep 数学宝典不断完善与进步的思想源泉与不竭动力! 我们期待您的参与!如有指正、补充、完善,请登陆 http://www.sharewithu.com/bbs/viewthread.php?tid=424178

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目录
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 86-!-item-!-187;#058&000060 ..................................................................... 10 140-!-item-!-187;#058&000076 ................................................................... 10 195-!-item-!-187;#058&000100 ................................................................... 10 300-!-item-!-187;#058&000133 ................................................................... 10 354-!-item-!-187;#058&000214 ................................................................... 11 408-!-item-!-187;#058&000218 ................................................................... 11 462-!-item-!-187;#058&000279 ................................................................... 11 563-!-item-!-187;#058&000288 ................................................................... 12 617-!-item-!-187;#058&000317 ................................................................... 12 672-!-item-!-187;#058&000324 ................................................................... 12 726-!-item-!-187;#058&000339 ................................................................... 13 781-!-item-!-187;#058&000341 ................................................................... 13 881-!-item-!-187;#058&000429 ................................................................... 13 935-!-item-!-187;#058&000511 ................................................................... 14 989-!-item-!-187;#058&000579 ................................................................... 14 1043-!-item-!-187;#058&000590 ................................................................. 14 1097-!-item-!-187;#058&000661 ................................................................. 15 1151-!-item-!-187;#058&000679 ................................................................. 15 1251-!-item-!-187;#058&000852 ................................................................. 15 1305-!-item-!-187;#058&000855 ................................................................. 16 1407-!-item-!-187;#058&000929 ................................................................. 16 1557-!-item-!-187;#058&001222 ................................................................. 16 1765-!-item-!-187;#058&002433 ................................................................. 16 1819-!-item-!-187;#058&002455 ................................................................. 17 1873-!-item-!-187;#058&002459 ................................................................. 17 1925-!-item-!-187;#058&002479 ................................................................. 17 2023-!-item-!-187;#058&002572 ................................................................. 18 2077-!-item-!-187;#058&002573 ................................................................. 18 2131-!-item-!-187;#058&002580 ................................................................. 18 2186-!-item-!-187;#058&002582 ................................................................. 19 2292-!-item-!-187;#058&002682 ................................................................. 19 2346-!-item-!-187;#058&002760 ................................................................. 19 2446-!-item-!-187;#058&002780 ................................................................. 19 2500-!-item-!-187;#058&002904 ................................................................. 19 2600-!-item-!-187;#058&002931 ................................................................. 20 2847-!-item-!-187;#058&003085 ................................................................. 20 3042-!-item-!-187;#058&003156 ................................................................. 20 3096-!-item-!-187;#058&003188 ................................................................. 20 3150-!-item-!-187;#058&003215 ................................................................. 21 3204-!-item-!-187;#058&003218 ................................................................. 21 3308-!-item-!-187;#058&003278 ................................................................. 21
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42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85.

3362-!-item-!-187;#058&003280 ................................................................. 22 3416-!-item-!-187;#058&003281 ................................................................. 22 3524-!-item-!-187;#058&003319 ................................................................. 22 3824-!-item-!-187;#058&003586 ................................................................. 23 3927-!-item-!-187;#058&003647 ................................................................. 23 3982-!-item-!-187;#058&003679 ................................................................. 23 4036-!-item-!-187;#058&003710 ................................................................. 23 4090-!-item-!-187;#058&003782 ................................................................. 24 4144-!-item-!-187;#058&003797 ................................................................. 24 4198-!-item-!-187;#058&003817 ................................................................. 24 4349-!-item-!-187;#058&003856 ................................................................. 25 4404-!-item-!-187;#058&003880 ................................................................. 25 4458-!-item-!-187;#058&003882 ................................................................. 25 4604-!-item-!-187;#058&003931 ................................................................. 26 4658-!-item-!-187;#058&003940 ................................................................. 26 4761-!-item-!-187;#058&003968 ................................................................. 27 4863-!-item-!-187;#058&004007 ................................................................. 27 4918-!-item-!-187;#058&004054 ................................................................. 27 4972-!-item-!-187;#058&004074 ................................................................. 27 5072-!-item-!-187;#058&004127 ................................................................. 27 5126-!-item-!-187;#058&004141 ................................................................. 28 5228-!-item-!-187;#058&004178 ................................................................. 28 5329-!-item-!-187;#058&004211 ................................................................. 28 5432-!-item-!-187;#058&004252 ................................................................. 29 5486-!-item-!-187;#058&004317 ................................................................. 29 5586-!-item-!-187;#058&004324 ................................................................. 29 5640-!-item-!-187;#058&004354 ................................................................. 30 5791-!-item-!-187;#058&004570 ................................................................. 30 6564-!-item-!-187;#058&004850 ................................................................. 30 6765-!-item-!-187;#058&004947 ................................................................. 31 6868-!-item-!-187;#058&005029 ................................................................. 31 6922-!-item-!-187;#058&005032 ................................................................. 31 6977-!-item-!-187;#058&005035 ................................................................. 32 7031-!-item-!-187;#058&005040 ................................................................. 32 7085-!-item-!-187;#058&005061 ................................................................. 32 7139-!-item-!-187;#058&005072 ................................................................. 32 7339-!-item-!-187;#058&005310 ................................................................. 33 7535-!-item-!-187;#058&005487 ................................................................. 33 7589-!-item-!-187;#058&005492 ................................................................. 33 7692-!-item-!-187;#058&005524 ................................................................. 34 7746-!-item-!-187;#058&005794 ................................................................. 34 7800-!-item-!-187;#058&005796 ................................................................. 34 7854-!-item-!-187;#058&005813 ................................................................. 35 7908-!-item-!-187;#058&005852 ................................................................. 35
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86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100 . 101 . 102 . 103 . 104 . 105 . 106 . 107 . 108 . 109 . 110 . 111 . 112 . 113 . 114 . 115 . 116 . 117 . 118 . 119 . 120 . 121 . 122 . 123 . 124 . 125 . 126 . 127 . 128 . 129 .

7962-!-item-!-187;#058&005867 ................................................................. 35 8062-!-item-!-187;#058&006016 ................................................................. 35 8117-!-item-!-187;#058&006040 ................................................................. 36 8171-!-item-!-187;#058&006095 ................................................................. 36 8271-!-item-!-187;#058&006138 ................................................................. 36 8325-!-item-!-187;#058&006143 ................................................................. 36 8570-!-item-!-187;#058&006483 ................................................................. 37 8624-!-item-!-187;#058&006485 ................................................................. 37 8775-!-item-!-187;#058&006653 ................................................................. 37 8829-!-item-!-187;#058&006700 ................................................................. 37 8932-!-item-!-187;#058&006783 ................................................................. 38 8986-!-item-!-187;#058&006790 ................................................................. 38 9040-!-item-!-187;#058&006792 ................................................................. 38 9094-!-item-!-187;#058&006821 ................................................................. 39 9148-!-item-!-187;#058&006857 ................................................................. 39 9205-!-item-!-187;#058&006882 ................................................................. 39 9262-!-item-!-187;#058&006890 ................................................................. 40 9889-!-item-!-187;#058&007222 ................................................................. 40 9943-!-item-!-187;#058&007224 ................................................................. 40 9997-!-item-!-187;#058&007246 ................................................................. 41 10051-!-item-!-187;#058&007251 ............................................................... 41 10578-!-item-!-187;#058&007600 ............................................................... 41 10635-!-item-!-187;#058&007601 ............................................................... 41 11067-!-item-!-187;#058&007824................................................................ 42 11121-!-item-!-187;#058&007826................................................................ 42 11229-!-item-!-187;#058&007982................................................................ 42 11432-!-item-!-187;#058&008149................................................................ 43 11488-!-item-!-187;#058&008235................................................................ 43 11543-!-item-!-187;#058&008310................................................................ 43 11595-!-item-!-187;#058&008332................................................................ 44 11649-!-item-!-187;#058&008377................................................................ 44 11703-!-item-!-187;#058&008423................................................................ 44 11804-!-item-!-187;#058&008456................................................................ 45 11954-!-item-!-187;#058&008495................................................................ 45 12295-!-item-!-187;#058&008940 ............................................................... 45 12397-!-item-!-187;#058&009033 ............................................................... 46 12685-!-item-!-187;#058&009461 ............................................................... 46 12975-!-item-!-187;#058&009772 ............................................................... 46 13029-!-item-!-187;#058&009789 ............................................................... 47 13274-!-item-!-187;#058&009989 ............................................................... 47 13661-!-item-!-187;#058&010116................................................................ 47 13762-!-item-!-187;#058&010132 ............................................................... 48 13817-!-item-!-187;#058&010140 ............................................................... 48 13872-!-item-!-187;#058&010142 ............................................................... 48
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130 . 131 . 132 . 133 . 134 . 135 . 136 . 137 . 138 . 139 . 140 . 141 . 142 . 143 . 144 . 145 . 146 . 147 . 148 . 149 . 150 . 151 . 152 . 153 . 154 . 155 . 156 . 157 . 158 . 159 . 160 . 161 . 162 . 163 . 164 . 165 . 166 . 167 . 168 . 169 . 170 . 171 . 172 . 173 .

14021-!-item-!-187;#058&010265 ............................................................... 49 14121-!-item-!-187;#058&010319 ............................................................... 49 14175-!-item-!-187;#058&010326 ............................................................... 49 14229-!-item-!-187;#058&010329 ............................................................... 49 14283-!-item-!-187;#058&010330 ............................................................... 50 14337-!-item-!-187;#058&010335 ............................................................... 50 14393-!-item-!-187;#058&010357 ............................................................... 50 14447-!-item-!-187;#058&010361 ............................................................... 50 14501-!-item-!-187;#058&010393 ............................................................... 51 14556-!-item-!-187;#058&010396 ............................................................... 51 14610-!-item-!-187;#058&010398 ............................................................... 51 14664-!-item-!-187;#058&010407 ............................................................... 52 14718-!-item-!-187;#058&010409 ............................................................... 52 14772-!-item-!-187;#058&010415 ............................................................... 52 14826-!-item-!-187;#058&010416 ............................................................... 53 14880-!-item-!-187;#058&010418 ............................................................... 53 14980-!-item-!-187;#058&010478 ............................................................... 53 15034-!-item-!-187;#058&010480 ............................................................... 53 15274-!-item-!-187;#058&010713 ............................................................... 54 15328-!-item-!-187;#058&010715 ............................................................... 54 15382-!-item-!-187;#058&010719 ............................................................... 54 15486-!-item-!-187;#058&010743 ............................................................... 55 15540-!-item-!-187;#058&010751 ............................................................... 55 15687-!-item-!-187;#058&010776 ............................................................... 55 15741-!-item-!-187;#058&010784 ............................................................... 55 15795-!-item-!-187;#058&010817 ............................................................... 56 15849-!-item-!-187;#058&010825 ............................................................... 56 15904-!-item-!-187;#058&010840 ............................................................... 56 15958-!-item-!-187;#058&010868 ............................................................... 56 16012-!-item-!-187;#058&010902 ............................................................... 57 16066-!-item-!-187;#058&010935 ............................................................... 57 16120-!-item-!-187;#058&010949 ............................................................... 57 16220-!-item-!-187;#058&011014................................................................ 58 16419-!-item-!-187;#058&011075................................................................ 58 16473-!-item-!-187;#058&011078................................................................ 58 16527-!-item-!-187;#058&011081................................................................ 59 16673-!-item-!-187;#058&011115 ................................................................ 59 16727-!-item-!-187;#058&011198................................................................ 59 16781-!-item-!-187;#058&011242................................................................ 59 16835-!-item-!-187;#058&011243................................................................ 60 16889-!-item-!-187;#058&011265................................................................ 60 16943-!-item-!-187;#058&011304................................................................ 60 17043-!-item-!-187;#058&011315................................................................ 61 17097-!-item-!-187;#058&011316................................................................ 61
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174 . 175 . 176 . 177 . 178 . 179 . 180 . 181 . 182 . 183 . 184 . 185 . 186 . 187 . 188 . 189 . 190 . 191 . 192 . 193 . 194 . 195 . 196 . 197 . 198 . 199 . 200 . 201 . 202 . 203 . 204 . 205 . 206 . 207 . 208 . 209 . 210 . 211 . 212 . 213 . 214 . 215 . 216 . 217 .

17151-!-item-!-187;#058&011360................................................................ 61 17205-!-item-!-187;#058&011383................................................................ 61 17259-!-item-!-187;#058&011402................................................................ 62 17313-!-item-!-187;#058&011410................................................................ 62 17370-!-item-!-187;#058&011434................................................................ 63 17563-!-item-!-187;#058&011544................................................................ 63 17617-!-item-!-187;#058&011567................................................................ 63 17723-!-item-!-187;#058&011591................................................................ 64 17777-!-item-!-187;#058&011599................................................................ 64 17831-!-item-!-187;#058&011633................................................................ 64 17933-!-item-!-187;#058&011666................................................................ 65 17987-!-item-!-187;#058&011677................................................................ 65 18041-!-item-!-187;#058&011685................................................................ 66 18095-!-item-!-187;#058&011720................................................................ 66 18293-!-item-!-187;#058&011863................................................................ 66 18439-!-item-!-187;#058&011934................................................................ 67 18493-!-item-!-187;#058&011993................................................................ 67 18547-!-item-!-187;#058&011999................................................................ 67 18601-!-item-!-187;#058&012081 ............................................................... 67 18701-!-item-!-187;#058&012184 ............................................................... 68 18755-!-item-!-187;#058&012205 ............................................................... 68 18858-!-item-!-187;#058&012264 ............................................................... 68 18962-!-item-!-187;#058&012363 ............................................................... 69 19016-!-item-!-187;#058&012397 ............................................................... 69 19116-!-item-!-187;#058&012496................................................................ 69 19170-!-item-!-187;#058&012498 ............................................................... 70 19224-!-item-!-187;#058&012506 ............................................................... 70 19278-!-item-!-187;#058&012507 ................................................................ 70 19378-!-item-!-187;#058&012570 ................................................................ 71 19527-!-item-!-187;#058&012646 ................................................................ 71 19581-!-item-!-187;#058&012650 ............................................................... 71 19960-!-item-!-187;#058&012914 ................................................................ 71 20297-!-item-!-187;#058&013111................................................................ 72 20351-!-item-!-187;#058&013123 ............................................................... 72 20405-!-item-!-187;#058&013127 ............................................................... 72 20459-!-item-!-187;#058&013172 ............................................................... 73 20513-!-item-!-187;#058&013256 ............................................................... 73 20614-!-item-!-187;#058&013294 ............................................................... 73 20668-!-item-!-187;#058&013295 ............................................................... 74 20722-!-item-!-187;#058&013303 ............................................................... 74 20776-!-item-!-187;#058&013419 ............................................................... 74 20830-!-item-!-187;#058&013425 ............................................................... 75 20930-!-item-!-187;#058&013466 ............................................................... 75 20984-!-item-!-187;#058&013473 ................................................................ 75
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218 .

21130-!-item-!-187;#058&013592................................................................ 76

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Practice Test #2 Data Sufficiency (218 Questions)
1. 86-!-item-!-187;#058&000060

Is m > k ? (1) 3m > 3k (2) 2m > 2k

题目翻译:不翻译 仅条件一:充分,保留 A、D 仅条件二:充分,排除 A 选择 D 难度评级:★★

2.

140-!-item-!-187;#058&000076

If k is a positive integer, is k the square of an integer? (1) k is divisible by 4. (2) k is divisible by exactly four different prime numbers.

题目翻译:k 是正数,它是完全平方数吗? 仅条件一:k 可以被 4 整除,无法推出,排除 A、D 仅条件二:k 可以被 4 个不同的质数整除,无法推出,排除 B 一二同看:无法推出,排除 C 选择 E 难度评级:★★

3.

195-!-item-!-187;#058&000100

If w and z are positive, is w/z < 1 ? (1) w < z (2) z < 4

题目翻译:w 和 z 是正数,w/z < 1 吗? 仅条件一:w < z,与原题一致,保留 A、D 仅条件二:无法推出,排除 D,选择 A 难度评级:★

4.

300-!-item-!-187;#058&000133

The sale price of a certain jacket was 15 percent less than its original price, and the sale price of a certain shirt was 10 percent less than its original price. How much greater was the original price of the jacket than the original price of the shirt? (1) The sale price of the jacket was $83 greater than the sale price of the shirt. (2) The original price of the jacket was $140.

题目翻译:夹克的卖价比原价低 15% ,衬衫的卖价比原价低 10% 。夹克的卖价比衬衫的卖
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价高多少? 仅条件一:夹克的卖价比衬衫的卖价高 83 美元,无解,排除 A、D 仅条件二:夹克的原价是 140 美元,无解,排除 B 一二同看:知道夹克的原价,可求出夹克的卖价,进一步求出衬衫的卖价, 再进一步求出衬 衫的原价,可以求出原题答案 难度评级:★★

5.

354-!-item-!-187;#058&000214

If x, y, and z are integers, is x + y + 2z even? (1) x + z is even. (2) y + z is even.

题目翻译:x、y、z 是整数,x + y + 2z 是偶数吗? 仅条件一:知道 x+z 是偶数,但不知道 y+z 的情况,无解,排除 A、D 仅条件二:知道 y+z 是偶数,但不知道 x+z 的情况,无解,排除 B 一二同看:x+z 和 y+z 都是偶然,可以推出所求式为偶数 难度评级:★

6. 0?

408-!-item-!-187;#058&000218

The operation @ represents either addition, subtraction, or multiplication of integers. What is the value of 1 @ (1) 0 @ 2 = 2 (2) 2 @ 0 = 2

题目翻译:@可以代表加、减、乘三种运算。1@0 的值是? 仅条件一:@只可能代表加法,原式有唯一解,保留 A、D 仅条件二:@可以代表加法或减法,原式仍然有唯一解,排除 A 选择 D 难度评级:★★★ Caution!:在看条件二的时候要很多人可以推断出@可以代表加法或减法,但往往忽视了这 两种情况下原式的解是一样的。

7.

462-!-item-!-187;#058&000279

One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8 ? (1) y > 0.15 (2) C ? 7.30

题目翻译:一种混合咖啡,一公斤的混合咖啡由 x 公斤的 I 咖啡和 y 公斤的 II 咖啡组成,售 价是 C 美元/公斤,C= 6.5x + 8.5y,问 x < 0.8 吗 仅条件一:y > 0.15 可以推出 x < 0.85,不充分,排除 A、D 仅条件二:因为一公斤 C 是 x 公斤 I 和 y 公斤 II,所以 x + y = 1,所以 C = 6.5x + 8.5(1-x) =
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8.5 – 2x,8.5 – 2x ? 7.30,2x ≤ 1.2,x ≤ 0.6,充分,选择 B 难度评级:★★★

8.

563-!-item-!-187;#058&000288

If n and p are integers, is p > 0 ? (1) n + 1 > 0 (2) np > 0

题目翻译:不翻译 仅条件一:n > -1,和 p 无关,不充分,排除 A、D 仅条件二:n、p 同号,不充分,排除 B 一二同看:n、p 同号,但 n 的符号也无法确定,故不充分,排除 C 选择 E 难度评级:★

9.

617-!-item-!-187;#058&000317

Each of the 105 students in a certain club is either a freshman, a sophomore, or a junior. How many of the students in the club are sophomores? (1) The ratio of the number of freshmen to the number of sophomores is 1 to 2. (2) The ratio of the number of freshmen to the number of juniors is 1 to 4.

题目翻译:105 个学生,要么是大一,要么是大二,要么是大三,其中有多少是大二的呢? 仅条件一:大一和大二的学生比例是 1:2,无法推出大三的情况,排除 A、D 仅条件二:大一和大三的学生比例是 1:4,无法推出大二的情况,排除 B 一二同看:大一大二大三学生的比例是 1:2:4,总量又已知,三个年级各有多少人不难求 出 难度评级:★★

10 . 672-!-item-!-187;#058&000324 Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy? (1) The total cost of the hardcover books that Juan bought was at least $150. (2) The total cost of all the books that Juan bought was less than $260.

题目翻译:J 买了一些平装书,每本 8 美元;他还买了一些精装书,每本 25 美元。如果 J 买了超过 10 本平装书,他买了多少本精装呢? 仅条件一:J 买的精装书的总价至少是 150 美元,只能得到 J 的精装书多于 6 本,无解,排 除 A、D 仅条件二:J 买的书的总价低于 260 美元,平装至少 88 美元,所以精装的价钱可以从 25 到 150 不等,本书从 1 本到 6 本不等,无解,排除 B 一二同看: 条件一得精装书至少 6 本, 条件二得精装书至多 6 本, 故 J 一定买了 6 本精装书, 有解,排除 E 选择 C。
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难度评级:★★★

11 . 726-!-item-!-187;#058&000339 What is the value of the positive integer m ? (1) When m is divided by 6, the remainder is 3. (2) When 15 is divided by m, the remainder is 6.

题目翻译:正整数 m 的值是多少? 仅条件一:m 被 6 除余 3,这样的数太多了,无解,排除 A、D 仅条件二:15 被 m 除余 6,m 只能是 9,有解,选择 B 难度评级:★★

12 . 781-!-item-!-187;#058&000341 Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three of the sets A, B, and C have in common? (1) Of the 16 elements that are in both A and B, 9 elements are also in C. (2) A has 25 elements, B has 30 elements, and C has 35 elements.

题目翻译:A、B、C 三个集合含有一些共同的元素。如果 16 个元素在 A 和 B 里都有,17 个元素在 A 和 C 里都有,18 个元素在 B 和 C 里都有。问 A、B、C 三个集合共有的元素有 多少? 仅条件一:画韦恩式图,如下所示。可以得到中间为 9,有解,保留 A、D

A

7

9 、

B

C

仅条件二:只知道 A、B、C 各有多少人,无法推出公共部分,无解,排除 D,选择 A 难度评级:★★★ Caution!:条件二有一点点绕,画图就一目了然了

13 . 881-!-item-!-187;#058&000429 Of the people who attended a workshop, 60 percent were teachers and some of the teachers were teachers of language arts. What percent of the people who attended the workshop were teachers of language arts?

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(1) 200 people attended the workshop. (2) 72 of the teachers who attended the workshop were not teachers of language arts.

题目翻译:参加修炼营的人中,有 60% 是老师,其中有些老师是教语言艺术的。问修炼营 中教语言艺术的老师占比多少? 仅条件一:知道总人数,可以算出老师的具体人数,但无法回答原题提出的问题,排除 A、 D 仅条件二:有 72 个老师不是讲语言艺术的,啥都算不出来,排除 B 一二同看:用总人数和 60% 可以求出老师的数量,减去非语言艺术的老师,可以得到教语 言艺术的老师数量,再除以总人数即可,选择 C 排除 E 难度评级:★

14 . 935-!-item-!-187;#058&000511 Jane walked for 4 miles. What was her average speed for the first 2 miles? (1) Jane's average speed for the 4 miles was 3.2 miles per hour. (2) It took Jane 15 minutes longer to walk the second 2 miles than it took her to walk the first 2 miles.

题目翻译:J 走了 4 英里,她前 2 英里的平均速度是多少? 仅条件一:J4 英里的平均速度是 3.2 英里/小时,只能求出时间是 1 小时 15 分钟,求不出前 2 英里的平均速度,无解,排除 A、D 仅条件二:J 走后 2 英里比走前 2 英里多花了 15 分钟,但不知道前 2 英里和后 2 英里各多 长时间,亦无解,排除 B 一二同看:条件一可求出总时间,条件二可求出两段分别的时间,随之即可求出速度 难度评级:★★

15 . 989-!-item-!-187;#058&000579 Is xy + xz = 0 ? (1) x = 0 (2) y + z = 0

题目翻译:xy + xz = 0 吗? 仅条件一:xy + xz =x*(y+z)=0,保留 A、D 仅条件二:xy + xz =x*(y+z)=0,选择 D 难度评级:★

16 . 1043-!-item-!-187;#058&000590 Is |K | = 2 ? (1) K2= 4 (2) K =∣-2∣

题目翻译:不翻译
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仅条件一:充分,保留 A、D 仅条件二:K=2,充分,选择 D 难度评级:★

17 . 1097-!-item-!-187;#058&000661 Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday? (1) Last week Store S sold 8 copies of the book on Thursday. (2) Last week Store S sold 38 copies of the book on Saturday.

题目翻译:S 店上周卖了 90 本书,并且 S 店每天卖的书的数量不相同。如果 S 店上周周六 卖的书最多,周五卖的书第二多,那么周五卖的书有没有超过 11 本? 仅条件一:上周四卖了 8 本,还剩下 82 本,可以是 60、12(周五) 、4、3、2、1,也可以 是 67、5(周五) 、4、3、2、1,无法确定,排除 A、D 仅条件二:上周六卖了 38 本,还剩下 52 本,而周五是剩下的 6 天里卖的最多的一天,假设 周五卖的数没有超过 11 本(以 11 本计算) ,剩下的 5 天最多是 10+9+8+7+6=40 本,共计 51 本,无法达到 52 本的既定数字,故周五的售数量必定超过 11 本,选择 B 难度评级:★★★

18 . 1151-!-item-!-187;#058&000679 Are the two nonzero integers x and y on opposite sides of 0 on the number line? (1) The sum of x and y is 0. (2) The product of x and y is less than 0.

题目翻译:两个非零整数 x 和 y 在数轴上是在 0 的两边吗?(即 x、y 异号吗?) 仅条件一:x 与 y 的和为 0,又因为两数非 0,一定等值异号,保留 A、D 仅条件二:x 与 y 的积为负,一定异号,排除 A 选择 D 难度评级:★

19 . 1251-!-item-!-187;#058&000852 Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T ? (1) The median of the numbers in set S is 0. (2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

题目翻译:集合 S 有 5 个连续整数,集合 T 有 7 个连续整数。S 里数字的中位数与 T 里数 字的中位数相等吗? 仅条件一:S 里数字的中位数是 0,但 T 里数字的情况不知道 仅条件二:S 和 T 里数字的和相等,如果和是 0 的话则两集合中位数相等,如果和不是零的 话则两集合中位数不等
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一二同看:S 的中位数是 0,S 的和一定是 0,S 和 T 的和相等,T 的和也是 0,又是连续整 数,中位数一定是 0 难度评级:★★★★

20 . 1305-!-item-!-187;#058&000855 If -2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y - 20 = 0

题目翻译:如果-2x > 3y ,x 是负数吗? 仅条件一:y > 0,则 3y > 0,-2x > 3y > 0,则 x 一定是负数,可以判断,保留 A、D 仅条件二: 把 2x 移至等式右侧可得-2x=5y-20, 代入原题得,5y-20 > 3y ,解得 y > 10,-2x > 3y >
30,则 x 一定是负数,可以判断,排除 A 选择 D

难度评级:★★

21 . 1407-!-item-!-187;#058&000929 Is the integer n odd? (1) n is divisible by 3. (2) 2n is divisible by twice as many positive integers as n.

题目翻译:n 是奇数吗? 仅条件一:n 可以被 3 整除,3 或 6 都可以,无法确定,排除 A、D 仅条件二:能整除 2n 的数是能整除 n 的数的两倍。 如果 n 是奇数,令 n=15,因子有 1、3、5、15,而 2n=30,因子有 1、3、5、15、2(1*2) 、 6(3*2) 、10(5*2) 、30(15*2) ,即,2n 的因子是 n 的每一个因子加上每一个因子乘以 2。 如果 n 是偶数,令 n=14,因子有 1、2、7、14,而 2n=28,因子有 1、2、7、14、2(1*2) 、 4(2*2) 、14(7*2) 、28(14*2) ,但是 2 与 14 是重复的,所以 2n 的因子数没有 n 的两倍。 故,n 必为奇数 难度评级:★★★★★

22 . 1557-!-item-!-187;#058&001222 Is [?]? (1) p = r (2) r > 0

23 . 1765-!-item-!-187;#058&002433

q q q q In the table above, is z = 20q ? q r s t (1) q = 3 q u v w (2) Each value in the table other than q is equal to the sum of the value immediately above it in the table and the q x y z 16 www.sharewithu.com

value immediately to its left in the table.

题目翻译:不翻译 仅条件一:显然不充分,排除 A、D 仅条件二:因为每个数都等于上面和左边数的和,那么假设 q 是 1,上表变为: 1 1 1 1 充分,选择 B 难度评级:★★ 1 2 3 4 1 3 6 10 1 4 10 20

24 . 1819-!-item-!-187;#058&002455 One member of a committee of 5 men and 8 women was resigned and was not replaced. What fraction of the remaining members were men? (1)7/12 of the remaining members were women. (2)The member who resigned was a woman.

题目翻译:一个委员会有 5 个男的和 8 个女的,有一个人被辞了但没有人替补,剩下的里有 多少是男的? 仅条件一:1-7/12=5/12,充分,保留 A、D 仅条件二:走的那个是女的,可以知道还剩下 12 个人,其中 5 个男的,充分,排除 A 选择 D 难度评级:★

25 . 1873-!-item-!-187;#058&002459 If x and y are greater than 0, is x = 1 ? (1) x/y=1 (2) xy=1

题目翻译:不翻译 仅条件一:x=y,不充分,排除 A、D 仅条件二:不充分,排除 B 一二同看:x^2=1,又因为 x 为正,所以 x=1 难度评级:★★

26 . 1925-!-item-!-187;#058&002479 If x and y are integers, is the value of x(y + 1) even? (1) x and y are prime numbers. (2) y > 7

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题目翻译:x(y+1)是不是偶数? 仅条件一:x,y 为质数,依然不知道奇偶性,条件不足,排除 A、D 仅条件二:Y 大于 7,条件不足,排除 B 一二同看:Y 大于 7,且为质数,则肯定是奇数,则 Y+1 必为偶数,偶数乘以任何数都为偶 数,则 x(y+1)为偶数,选择 C 难度评级:★★
27 . 2023-!-item-!-187;#058&002572 Does set S contain any even numbers? (1) There are no prime numbers in S. (2) There are no multiples of 4 in S.

题目翻译:集合 S 中有木有偶数? 仅条件一:集合中木有质数。质数包括 2 和一部分奇数,集合中木有质数只能说明不含有部 分奇数,可能全部都是奇数的合数,不能保证有偶数。排除 A、D 仅条件二:集合中木有 4 的倍数。不是 4 的倍数,不一定不是 2 的倍数,因此无法判断集合 中是否有偶数,排除 B 一二同看:根据条件一,排除集合 S 中含有 2 和一部分奇数;根据条件二,排除 4 的倍数, 但是依然无法确定集合中是否含有偶数,例如 6。 难度评级:★★

28 . 2077-!-item-!-187;#058&002573 A certain movie depicted product A in 21 scenes, product B in 7 scenes, product C in 4 scenes, and product D in 3 scenes. The four product manufacturers paid amounts proportional to the number of scenes in which their product was depicted in the movie. If each manufacturer paid x dollars per scene, how much did the manufacturer of product D pay for this advertising? (1) The manufacturers of products A and B together paid a total of $560,000 for this advertising. (2) The manufacturer of product B paid $60,000 more for this advertising than the manufacturer of product C paid.

题目翻译:某影片用 21 个场景拍摄产品 A,7 个场景拍产品 B,4 个场景拍产品 C,3 个场 景拍产品 D。 4 个产品的制造商按照影片中场景的比例支付报酬.如果每个制造商给每个场景 付 X 块钱,D 制造商付了多少钱? 仅条件一:A 和 B 拍摄场景一共 28 个,需要付 28X=560000,则可以求出 X=20000,那么 D 需要支付 3X=60000。有解,保留 A、D 仅条件二:B 比 C 多付 60000,也就是 7X-4X=60000,求出 X=20000,一样可以求出 D 需 要付的金额。有解,选择 D 难度评级:★

29 . 2131-!-item-!-187;#058&002580 Is the positive integer n odd? (1) n = 2k + 1, where k is a positive integer. (2) 2n + 1 is an odd integer.

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题目翻译:正整数 n 是奇数咩? 仅条件一:根据 n 的表达式,可知 n 为奇数,保留 A、D 仅条件二:2n+1 是奇数,则 2n 为偶数,无法判断 n 的奇偶,排除 B,选择 A 难度评级:★★

30 . 2186-!-item-!-187;#058&002582 If n is an integer, is n/7 an integer? (1) 3n/7 is an integer. (2) 5n/7 is an integer.

题目翻译:不翻译 仅条件一:3 不能被 7 整除,n 一定可以被 7 整除,充分,保留 A、D 仅条件二:5 不能被 7 整除,n 一定可以被 7 整除,充分,排除 A 选择 D 难度评级:★

31 . 2292-!-item-!-187;#058&002682 If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece? (1) The length of the longest piece is twice the length of the shortest piece. (2) The sum of the lengths of the two shorter pieces is 15 meters.

题目翻译:一段 27 米长的线被切成了三段不等长度,最长的线多长? 仅条件一:最长的线是最短的线的两倍长,条件不足,无解,排除 A、D 仅条件二:较短的两根线长度之和是 15 米,则最长的线长度为 27-15=12 米,选择 B 难度评级:★

32 . 2346-!-item-!-187;#058&002760 Is positive integer n divisible by 3 ?

33 . 2446-!-item-!-187;#058&002780 If a > 0, b > 0, and c > 0, is a(b - c) = 0 ?

34 . 2500-!-item-!-187;#058&002904 Are positive integers p and q both greater than n ? (1) p - q is greater than n . (2) q > p

题目翻译:正整数 p 和 q 都比 n 大么? 仅条件一:p-q 比 n 大,只能知道 P 比 n 大,条件不足,排除 A、D
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仅条件二:知道 q 比 p 大,还是不知道是否比 n 大,条件不足,排除 B 一二同看:q 比 p 大,则 p-q<0,那么 n<0,则 p,q 两个正整数一定比 n 大,选择 C 难度评级:★★

35 . 2600-!-item-!-187;#058&002931 What is the value of xy ? (1) y = x + 1 (2) y = x^2+ 1

题目翻译:不翻译 仅条件一:不充分,排除 A、D 仅条件二:不充分,排除 B 一二同看:联立,得 x=1 或 0,不允许,排除 C 选择 E 难度评级:★★

36 . 2847-!-item-!-187;#058&003085 If ax + b = 0, is x > 0 ? (1) a + b > 0 (2) a - b > 0

题目翻译:不解释 仅条件一:x=-b/a,判断 x 的符号要看 ab 是否同号。条件一无法判断,排除 A、D 仅条件二:条件二无法判断,排除 B 一二同看:结合一二,可以得出 a>0,但是 b 的符号无法判断,选择 E 难度评级:★★

37 . 3042-!-item-!-187;#058&003156 Are the integers z and f to the right of 0 on the number line? (1) The product of z and f is positive. (2) The sum of z and f is positive.

题目翻译:整数 z 和 f 在数轴上是否在 0 的右边,即 z 和 f 是否大于 0? 仅条件一:zf>0,只能判断 zf 同号,条件不足,排除 A、D 仅条件二:z+f>0,无法判断,条件不足,排除 B 一二同看:zf 同号且和大于 0,可以判断 z 和 f 都大于 0,选择 C 难度评级:★★

38 . 3096-!-item-!-187;#058&003188 Some of the students enrolled at College T are part-time students and the rest are full-time students. By what percent did the number of full-time students enrolled at College T increase from the fall of 1999 to the fall of

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2000 ? (1) There were 50 more full-time students enrolled at College T in the fall of 2000 than in the fall of 1999. (2) The total number of students enrolled at College T increased by 5 percent from the fall of 1999 to the fall of 2000.

题目翻译:T 录取的学生中有一部分是业余的,其他的是全职的。问从 1999 年秋天到 2000 年秋天,全职学生的数量增加了多少比例? 仅条件一:2000 年比 1999 年多录取了 50 个全职学生。只知道数量,不知道总数,无解, 排除 A、D 仅条件二:1999 年到 2000 年学生总数增加了 5% 。只知道学生总数,条件不足,排除 B 一二同看: 要求全职学生增加的比例, 但是现在只知道全职学生增加的量和总人数增加的比 例,条件依然不足,无解,选择 E 难度评级:★★

39 . 3150-!-item-!-187;#058&003215 If c and d are integers, is c even? (1) c(d + 1) is even. (2) (c + 2)(d + 4) is even.

题目翻译:不解释 仅条件一:只能判断 c 是偶数或者 d 是奇数,条件不足,排除 A、D 仅条件二:只能判断 c 或者 d 中其中一个或者两者都为偶数,条件不足,排除 B 一二同看:结合一二,可得 C 为偶数,选择 C 难度评级:★★

40 . 3204-!-item-!-187;#058&003218 If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ? (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1.

题目翻译:集合 S 包括这么一列数,问 n 的范围 仅条件一: 这列数的中数小于 5。按照已知数字排列顺序应该是:-2, 1,5,8, 如果中数小于 5, 那么中数只能为 1,或者 n,且 n<5,但是不能确定 n 是否大于 0,条件不足,排除 A、D 仅条件二:S 的中数大于 1。则中数只能为 5,或者 n, 且 n>1,但是无法确定 n 是否小于 7, 条件不足,排除 B 一二同看:结合一二,可知中数只能为 n,且 1<n<5,则可以确定 0<n<7。选择 C 难度评级:★★★

41 . 3308-!-item-!-187;#058&003278 Last Thursday, John assembled chairs at a rate of 3 chairs per hour for part of the day and Larry assembled no chairs. Last Friday, Larry assembled chairs at a rate of 4 chairs per hour for part of the day and John assembled

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no chairs. If John and Larry assembled chairs for a total of 7 hours during these two days, how many chairs did John assemble last Thursday? (1) During these two days, John and Larry assembled a total of 25 chairs. (2) During these two days, Larry assembled more chairs than John did.

题目翻译:上周四,J 以每小时 3 把椅子的速度组装椅子,L 木有干活。上周五,L 以每小 时 4 把椅子的速度组装椅子, J 木有干活。 如果 J 和 L 在这两天里一共干了 7 个小时的活儿, 那么 J 上周四组装了多少椅子? 仅条件一:这两天,J 和 L 一共组装了 25 把椅子。假设 J 工作了 X 个小时,L 工作了 Y 小 时,那么可列出方程组:X+Y=7; 3X+4Y=25。可求出 XY 的值,进而求出 J 组装的椅子,有 解,保留 A、D 仅条件二:这两天,L 组装的椅子比 J 多。说了跟没说一样,无解,排除 B,选择 A 难度评级:★

42 . 3362-!-item-!-187;#058&003280 What is the value of 3n - 4 ? (1) 6n-10=30 (2) n/3=20/9

题目翻译:不翻译 仅条件一:3n=20,充分,保留 A、D 仅条件二:3n=20,充分,排除 A 选择 D 难度评级:★

43 . 3416-!-item-!-187;#058&003281 Circle C and line k lie in the xy-plane. If circle C is centered at the origin and has radius 1, does line k intersect circle C ? (1) The x-intercept of line k is greater than 1. (2) The slope of line k is

44 . 3524-!-item-!-187;#058&003319 How many people received a certain survey? (1) Six-tenths of those who received the survey responded. (2) Of those who received the survey, 42 responded.

题目翻译:多少人接受了调查? 仅条件一:十分之六接受调查的人反馈了。条件不足,排除 A、D 仅条件二:接受调查的人中,42 个反馈了。条件不足,排除 B 一二同看:0.6X=42,求出 X=70。有解,选择 C。 难度评级:★

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45 . 3824-!-item-!-187;#058&003586 If x and z are integers, is at least one of them even? (1) x + z is odd. (2) x - z is odd.

题目翻译:X 和 Z 都是整数,是否其中至少一个为偶数 思路:偶数+/-偶数=偶数,奇数+/-奇数=偶数,奇数+/-偶数=奇数 仅条件一:X+Z 为奇数 说明 X 和 Z 中一奇一偶 充分 仅条件二:X-Z 为奇数 说明 X 和 Z 中一奇一偶 充分 难度评级:★

46 . 3927-!-item-!-187;#058&003647 Three thousand families live in a certain town. How many families who live in the town own neither a car nor a television set? (1) Of the families who live in the town, 2,980 own a car. (2) Of the families who live in the town, 2,970 own both a car and a television set.

题目翻译:3000 户家庭,有多少家庭既没有车又没有电视 思路:设 X=只有车,Y=只有电视,Z=有车有电视,W=无车无电视。X+Y+Z+W=3000, W=? 仅条件一:X+Z=2980 不充分 仅条件二:Z=2970 不充分 一二一起: 可得 X 和 Z,但仍然退不出 W,不充分,选 E 难度评级:★

47 . 3982-!-item-!-187;#058&003679 In the fraction [?], where x and y are positive integers, what is the value of y ?

48 . 4036-!-item-!-187;#058&003710 There are two types of rolls on a counter, plain rolls and seeded rolls. What is the total number of rolls on the counter? (1) The ratio of the number of seeded rolls on the counter to the number of plain rolls on the counter is 1 to 5. (2) There are 16 more plain rolls than seeded rolls on the counter.

题目翻译:两种 rolls, P 和 S, P+S=? 仅条件一:S/P=1/5 不充分 仅条件二:P-16=S 充分 选B 难度评级:★

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49 . 4090-!-item-!-187;#058&003782 Is the hundredths digit of the decimal d greater than 5 ? (1) The tenths digit of 10d is 7. (2) The thousandths digit of d/10 is 7.

题目翻译:d 的百分位比 5 大吗? 仅条件一:10d 的十分位就是 d 的百分位,充分,保留 A、D 仅条件二:d/10 的千分位就是 d 的百分位,充分,排除 A 选择 D 难度评级:★

50 . 4144-!-item-!-187;#058&003797 What is the value of 2x + 2y ? (1) (2) 3x + 5y = 60 5x + 3y = 68

题目翻译:2X+2Y=? 仅条件一:2x+2y+x+3y=60, 不充分 仅条件二:不充分 一二一起 : 联立解出 x 和 y,得出 2x+2y, 充分 选C 难度评级:★

51 . 4198-!-item-!-187;#058&003817 Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martin's most recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill greater than 15 percent of the amount of the bill? (1) The amount of the bill was between $15 and $50. (2) The tip calculated by Martin was $8.

题目翻译: 当账单金额在 10-99 刀之间,小费为账单金额十位数的两倍。 问,是否小费>15% 账单金额? 思路:设账单金额十位数为 X,个位数为 Y。 故求 2x>15% (10X+Y) 仅条件一: 知道总额位于 15~50,如为 15 => 2<2.25 如为 50 => 10 >7.5 无其他信息缩小范 围, 不充分 仅条件二:已知小费为 8,所以总额的区间缩小到 40~49。取最大最小值来计算: 8 > 0.15(40) 且 8>0.15(49) 所以即可推出所求 充分 选B 难度评级:★★

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52 . 4349-!-item-!-187;#058&003856 For Manufacturer M, the cost C of producing x units of its product per month is given by C = kx + t, where C is in dollars and k and t are constants. Last month, if Manufacturer M produced 1,000 units of its product and sold all the units for k + 60 dollars each, what was Manufacturer M's gross profit on the 1,000 units? (1) Last month, Manufacturer M's revenue from the sale of the 1,000 units was $150,000. (2) Manufacturer M's cost of producing 500 units in a month is $45,000 less than its cost of producing 1,000 units in a month.

题目翻译:x=1000units,价格=k+60 思路:利润=收入-成本=[k+60-(1000k+t)]*1000 仅条件一:Revenue = Gross Profit – Expense,无法得知营业费用所以无法求出毛利, 不 充分 仅条件二:由此条件可得知 500k+t+45000 = 1000k+t 可求出 k 但无法求出 t,不充分 一二同看:仍然无法算出 t,故不充分,选 E 难度评级:★★

53 . 4404-!-item-!-187;#058&003880 The symbol @ represents one of the four arithmetic operations: addition, subtraction, multiplication, and division. Is (5 @ 6) @ 2 = 5 @ (6 @ 2) ? (1) 5 @ 6 = 6 @ 5 (2) 2 @ 0 = 2

题目翻译:@代表加号,减号,乘号和除号。(5 @ 6) @ 2 = 5 @ (6 @ 2) ? 思路:如果该式不受()影响,@必须为 addition (+) 或 multiplication (X) 。因为先除后除会

5 5 影响分母=> (5 ? 6) ? 2 = 12 vs. 5 ? (6 ? 2)= 3 ,先减后减会影响正负数 =>(5 - 6) - 2 =
-3 vs. 5-(6-2)=1 仅条件一:已知 5 @ 6 = 6 @ 5 => @ 为 + 或 X =>因而可推出(5 @ 6) @ 2 = 5 @ (6 @ 2) 成立, 不充分 仅条件二:已知 2 @ 0 = 2 => @ 为+ 或 –,但如果@ 为 – 则题目的公式不成立。不充 分 一二一起看:仍然无法算出 t,故不充分,选 E 难度评级:★★

54 . 4458-!-item-!-187;#058&003882 If y is an integer and y = |x | + x, is y = 0 ? (1) x < 0 (2) y < 1

题目翻译:如果 y 是整数,y=|x |+x, y=0? 思路:若 x 为负数,则 y=0. 若 X 为正数,y=2x
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仅条件一:可推出 y=0 ,充分 仅条件二:已知 y < 1 , 且 y 为整数 => y

?

0 ; 如果 x 为负数 则可求得 y = 0 , 假设 x

为正数 => y=2x 此式不可能成立 (就算 x 不一定为整数,但在条件 1.y 必为整数 2. y x 根本不可能为正数 (ex: x=0.5,相加为 1 仅可满足条件 y 为整数,但和 y => 推论: 在此条件下, y 一定等于 0 充分 选D 难度评级:★★

?

0

?

0 条件不合。

55 . 4604-!-item-!-187;#058&003931 Is the positive integer n an odd integer? (1) n + 4 is a prime number. (2) n + 3 is not a prime number.

题目翻译:是否正整数 n 是奇数 思路:1. 奇数+奇数=偶数 偶数+偶数=偶数 奇数+偶数=奇数 2. 质数中的偶数只有 2 仅条件一:已知两数相加有一数为偶数且合为质数,从题目得知 n 为正整数 =>可得知 n 一 定不会为偶数(因质数中唯一的偶数为 2,正整数 n+4 一定大于 2) 所以 n 为奇数,充分 仅条件二:已知两数相加有一数为奇数且合一定不为质数,从题目得知 n 为正整数 => 因 两数相加有可能为奇数也有可能为偶数,所以无法确定 n 为奇数或偶数 不充分 选A 难度评级:★★

56 . 4658-!-item-!-187;#058&003940 What is the total surface area of rectangular solid R ? (1) The surface area of one of the faces of R is 48. (2) The length of one of the edges of R is 3.

题目翻译:R 长方体的表面积 思路:求长方体表面积的公式为: 2(长*宽+长*高+宽*高) 仅条件一:其中一面为 48,显然不充分 仅条件二:一条边为 3. 仍然不充分 一二同看:无法确定得知的那一边和已知的面积 48 信息有没有重复=> 无法得知长、宽、 高,不充分,选 E 难度评级:★

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57 . 4761-!-item-!-187;#058&003968 A certain list consists of several different integers. Is the product of all the integers in the list positive? (1) The product of the greatest and smallest of the integers in the list is positive. (2) There is an even number of integers in the list.

题目翻译:一个数列由几个不同的整数组成。这些整数的乘积是否为正? 仅条件一:最大数和最小数的乘积为正,但不知道其他的数,不充分 仅条件二:总共有偶数个数字. 仍然不充分 一二一起看: 因为是偶数个数字, 那么剔除掉最大值和最小值后生效的数的乘积一定为正数, 正数再乘以正数,一定为正,充分。选 C 难度评级:★★

58 . 4863-!-item-!-187;#058&004007 A certain store sells chairs individually or in sets of 6. The store charges less for purchasing a set of 6 chairs than for purchasing 6 chairs individually. How much does the store charge for purchasing a set of 6 chairs? (1) The charge for purchasing a set of 6 chairs is 10 percent less than the charge for purchasing the 6 chairs individually. (2) The charge for purchasing a set of 6 chairs is $20 more than the charge for purchasing 5 chairs individually.

题目翻译:一次批发 6 张椅子比单独购买 6 张椅子便宜,那么一次批发 6 张椅子多少钱 仅条件一:假设个别一张椅子的价格为 x 元, 则由此条件可得知 6 张一组的价格可由 0.9 ? 6x 来表示。但无其他信息可求得 x,不充分 仅条件二:由此选项可得知 5x+20 会等于 6 张一组的价格,但无其他信息可求得 x. 仍然不 充分 一二一起看: 0.9? 6x = 5x+20 => 0.4x = 20,可求出 x 的值即可求出 6 张一组的特惠价, 充分。 选C 难度评级:★

59 . 4918-!-item-!-187;#058&004054 If k [?] 0, 1, or -1, is > 0 ?

60 . 4972-!-item-!-187;#058&004074 Does the integer k have a factor p such that 1 < p < k ? (1) k > 4! (2) 13! + 2 [?] k [?] 13! + 13

61 . 5072-!-item-!-187;#058&004127 When the positive integer n is divided by 25, the remainder is 13. What is the value of n ? (1) n < 100

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(2) When n is divided by 20, the remainder is 3.

题目翻译:n=25m+13 仅条件一:n<100,可得 m<4,即 m 为 1 或 2 或 3,但无法确定 n 值, 不充分 仅条件二:得知 n = 20p + 3 = 25x +13 => 5m–4p+2=0 且 p 为大于 0 的整数;但无另一方 程式可分求 m,p 仍然不充分 一二一起看:将 m =1 代入 => 5-4p+2=0, p 非整数所以不对 ; m=2 代入得到 10-4p+2=0.p=3 ; m=3 代入 =>15-4p+2=0 ,y 整数不对。所以只有一解 m=2,p=3 带回方程式即可求得 n。*另 一个快速解 : 5x-4y+2=0 如 y 要为整数,x 一定要为偶数。原因: 奇数(5)? 偶数才会等于偶 数,而偶数除于偶数才有可能可求得整数=>可用此想法来减少 x 的范围。充分,选 C 难度评级:★★

62 . 5126-!-item-!-187;#058&004141 If y ? 0, what is the value of x ? (1) |x - 3| ? y (2) |x - 3| ≤ -y

题目翻译:不翻译 仅条件一:|x - 3| ? y ? 0,不充分,排除 A、D 仅条件二:|x - 3| ≤ -y ≤ 0,因为绝对值非负,故只能为 0,故 x=3,充分,选择 B 难度评级:★★★

63 . 5228-!-item-!-187;#058&004178 If m is a positive odd integer, what is the average (arithmetic mean) of a certain set of m integers? (1) The integers in the set are consecutive multiples of 3. (2) The median of the set of integers is 33.

题目翻译:m 为正奇数,求连续 m 个整数的平均值 仅条件一:这个数列中的整数是连续的 3 的倍数。可知前后两数之间差 3,但由于不知道 m 为多少,所以无法求得平均值。 不充分 仅条件二:中数为 33,但不知道其他规律,仍然不充分 一二一起看: 平均值的公式为 m 个数相加除于 m。 已知中数为 33,则该列数可知总和为: m ? 33 (?(33-3 ? 2)+(33-3 ? 1)+33+(33+3 ? 1)+(33+3 ? 2)+? => 33 前后一定会有个相对称的

33m ? 3 ? 1, ? 3 ? 2? ) 套上平均值= m =33 充分,选 C
难度评级:★★★

64 . 5329-!-item-!-187;#058&004211 If a < y < z < b, is |y - a | < |y - b | ? (1) |z - a | < |z - b |

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(2) |y - a | < |z - b |

题目翻译:如果 a < y < z < b,是否 |y - a | < |y - b | ? 这题用距离的概念来想绝对值比较容易解。已知 a,y,z,b 在数在线的分布如下 仅条件一:在此条件下知道 az < zb ( yb = yz + zb 且 az = ay + yz )=> ay < az < zb < yb a y z b =>|y - a | < |y - b |, 充分 仅条件二:在此条件下知道 ay < zb => ay < yb (因 yb > zb ) => |y - a | < |y - b | ,充分 选D 难度评级:★★

65 . 5432-!-item-!-187;#058&004252 If ab is not 0 and points (-a, b) and (-b, a) are in the same quadrant of the xy-plane, is point (-x, y) in this same quadrant? (1) xy > 0 (2) ax > 0

题目翻译:如果 ab 不等于 0, (-a, b)和(-b,a)在同一个象限,ab 同正或同负。那么(-x,y) 是否在这个个象限 仅条件一:xy>0,x 和 y 同正同负,但不知道是否和 a,b 同号,不充分 仅条件二:ax 同号,说明 a 和 x 同号,但不知道是否与 y 同号,不充分 一二一起:则可以判断 a,b,x,y 一定同正或同负,故(-x,y)与(-a,b)在同一象限。充分 难度评级:★

66 . 5486-!-item-!-187;#058&004317 If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r ? (1) q > 10 (2) q = 2^k, where k is a positive integer.

题目翻译:如果 q 是正整数且小于 17,那么 17 除以 q 的余数为多少 仅条件一:q>10,那么 q 是 11 或 12 或 13 或 14 或 15 或 16,无法判断余数,不充分 仅条件二:q=2^k,q 有可能为 2,4,8,16, 而 17 除以这些数的余数都是 1 选 B,充分 难度评级:★

67 . 5586-!-item-!-187;#058&004324 What is the ratio of the number of cups of flour to the number of cups of sugar required in a certain cake recipe? (1) The number of cups of flour required in the recipe is 250 percent of the number of cups of sugar required in the recipe.

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(2) [?]

68 . 5640-!-item-!-187;#058&004354 In 1999 Company X's gross profit was what percent of its revenue? (1) In 1999 Company X's gross profit was 1/3 of its expenses. (2) In 1999 Company X's expenses were were 3/4 of its revenue.

题目翻译:99 年 X 公司的利润是收益的百分之多少 仅条件一:利润是成本的 1/3,可求得利润是收益的 1/4,充分,保留 A、D 仅条件二:成本是收益的 3/4,亦可求得利润是收益的 1/4,充分,排除 A 选择 D 难度评级:★★

69 . 5791-!-item-!-187;#058&004570 At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy? (1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes. (2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.

题目翻译:Lew 在面包店花了总共 6 刀,买了一种杯子蛋糕和一种甜甜圈。问他买了几个甜 甜圈? 仅条件一:有两个未知数,只有一个等式,无法推出 仅条件二:有两个未知数,只有一个等式,无法推出 一二同看:两个等式结合起来,结果是相互抵消,还是无法推出 选 E 难度评级:★ Caution!:两个等式结合起来的时候要注意,不要以为两个未知数,两个等式就一定有解。

70 . 6564-!-item-!-187;#058&004850 If eleven consecutive integers are listed from least to greatest, what is the average (arithmetic mean) of the eleven integers? (1) The average of the first nine integers is 7. (2) The average of the last nine integers is 9.

题目翻译:如果 11 个连续的整数从小到大排列,哪一个是他们的算数平均数 设:11 个数是 A1 <A2<??<A11 且 An 是以 1 为公差的等差数列 仅条件一:A1+A2+??A9=7*9=63 设为 1 式。不能算 仅条件二:A11+A10+A9+、 、 、+A3=81 设为 2 式。不能算 一二同看:2 式-1 式,A11+A10-A2-A1=18 又因为是等差数列,An 都可以用 A1 表示,所 以连个条件一起可以解。 C 难度评级:★ Caution!:不要看漏 consecutive

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71 . 6765-!-item-!-187;#058&004947 What is the greatest integer that is less than t ? (1) t=9/4 (2) t=(-3/2)^2

题目翻译:比 t 小的最大整数是多少? 仅条件一:充分,保留 A、D 仅条件二:算得 t=9/4,充分,排除 A 选择 D 难度评级:★

72 . 6868-!-item-!-187;#058&005029 Of the 4,800 voters who voted for or against Resolution K, 1800 were Democrats and 3,000 were Republicans. What was the total number of female voters who voted for Resolution K ? (1) 3/4 of the Democrats and 2/3 of the Republicans voted for Resolution K. (2) 1/3 of the Democrats who voted for Resolution K and 1/2 of the Republicans who voted for Resolution K were females.

题目翻译:4800 个投票支持或反对议案 K 的人里,1800 是民主党人,3000 个是共和党人。 那么,支持议案的女议员有多少人? 仅条件一:3/4 的民主党人和 2/3 的共和党人支持 K 议案,只知道支持的人有多少,不充分, 排除 A、D 仅条件二:1/3 支持 K 议案的民主党人和 1/2 支持 K 方案的共和党人是女性,不充分,排除 B 一二同看:一求支持人数,二求支持的女性,充分,排除 E 选择 C 难度评级:★★

73 . 6922-!-item-!-187;#058&005032 If n is a positive integer, is n^3 - n divisible by 4 ? (1) n = 2k + 1, where k is an integer. (2) n^2 + n is divisible by 6.

题目翻译:如果 N 是正整数,n^3 – n 可以被 4 整除吗? 仅条件一:n^3 – n=8K^3+12K^2+6K+1-(2K+1)= 8K^3+12K^2+4K 可以被 4 整除 仅条件二:因为(n^2+n)(n-1)=n^3-n, 因为 n^2 + n 可以被 6 整除,那么 n^2 + n 肯定包含一个 2 的因子,那么我们只用讨论 n-1 这
个能不能被 2 整除了。 n-1 要被 2 整除,只能说明 n 是奇数。但是条件没有说 n 是奇数,所以这个条件单独不成立。

一二同看:如果条件 1 单独可以成立,答案肯定就不是 C 了。所以不用考虑两个条件。 选A 难度评级:★ Caution!:如果条件 1 单独可以成立,答案肯定就不是 C 了。所以不用考虑两个条件。

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74 . 6977-!-item-!-187;#058&005035 If x ≠ -y, is (x-y)/(x+y) > 1 (1) x > 0 (2) y < 0

题目翻译:不翻译,将原式移项,(x-y-x-y)/(x+y)>0,y/(x+y)<0 仅条件一:不充分,不知道 y 的情况,排除 A、D 仅条件二:不充分,不知道 x 的情况,排除 B 一二同看:不充分,不知道分母是正是负,排除 C 选择 E 难度评级:★

75 . 7031-!-item-!-187;#058&005040 A certain group of car dealerships agreed to donate x dollars to a Red Cross chapter for each car sold during a 30-day period. What was the total amount that was expected to be donated? (1) A total of 500 cars were expected to be sold. (2) 60 more cars were sold than expected, so that the total amount actually donated was $28,000.

题目翻译:一群汽车代理商同意向红十字会捐钱, ,是根据一个周期卖的车来决定的,卖一 辆捐 X 元,这个周期是 30 天。问一共可以捐多少钱。 仅条件一:有 500 辆车会被卖。 那么捐款总数就是 500X 仅条件二:设预期卖 Y 辆 则可以列方程: (Y+60)X-XY=28000,这样就可以算出 Y, 一二同看: 难度评级:★选 D Caution!:X 是参数,不是未知数。

76 . 7085-!-item-!-187;#058&005061 Over a certain time period, did the number of shares of stock in Ruth's portfolio increase? (1) Over the time period, the ratio of the number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased. (2) Over the time period, the total number of shares of stocks and bonds in Ruth's portfolio increased.

题目翻译:一段时间后,R 这个人的股票投资组合的数量增加了吗? 仅条件一:stock/( stock+bond) 比例增加了。 有可能是 BOND 减少了。 仅条件二:stock+bond 增加了。 有可能只是 BOND 增加了。 一二同看:在 stock+bond 这个总量增加的情况下,stock/( stock+bond)这个比例还增加了, 所以说 stock 肯定也是增加了的。 难度评级:★ 选 C

77 . 7139-!-item-!-187;#058&005072 Is |x | = y - z ?

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(1) x + y = z (2) x < 0

题目翻译:RT 仅条件一:x=z-y 当 X<0 时,成立,当 X>0 时,不成立,有两种情况,所以不能选。 仅条件二:单独无法得出。 一二同看:锁定了 X<0 的情况,选 C 难度评级:★ Caution!:GMAT 数学题答案有唯一性,同一个条件出现两种解是错的。

78 . 7339-!-item-!-187;#058&005310 If n is an integer, is -3xn positive? (1) x is negative. (2) n is odd.

题目翻译:如果 n 是整数的话,-3xn 是正的吗? 仅条件一:x 是负数,但 xn 的正负不确定,不充分,排除 A、D 仅条件二:n 为奇,x 为正数时 xn 为正,x 为负数时 xn 为负,不充分,排除 B 一二同看:xn 一定是负数,原式一定是正数 难度评级:★★

79 . 7535-!-item-!-187;#058&005487 If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n ? (1) n is even. (2) The cube root of n is an integer.

题目翻译:N 是 2-100 之间的整数,如果 n 也是一个整数的平方。N 是多少 仅条件一:N 是偶数, 解太多了,不能选 仅条件二:N 的立方根也是整数。 设这个立方根是 K,由于条件没有说是 inclusive, 所以 2<K^3<100, K 只能是 3,4。那么 N 可能是 27 跟 64.但是 27 不是一个证书的平方根,所以只 有 64.唯一解。 一二同看:B 单独足矣。 选 B 难度评级:★
80 . 7589-!-item-!-187;#058&005492 If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y ? (1) x = 12u, where u is an integer. (2) y = 12z, where z is an integer.

题目翻译:XY 都是正整数,满足 x = 8y + 12,那么 XY 最大公约数是多少 比较最大公约数,最重要的是把两个数用同一个字母表示出来 仅条件一:x=12u,y=12(u-1)/8=3/2u-1/8 看不出来有整约数
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仅条件二:y=12Z,x=96z+12=12(8z+1) 因为 8z+1 跟 z 肯定互斥,所以 XY 最大公约是 12. 难度评级:★

81 . 7692-!-item-!-187;#058&005524 At a certain bakery, each roll costs r cents and each doughnut costs d cents. If Alfredo bought rolls and doughnuts at the bakery, how many cents did he pay for each roll? (1) Alfredo paid $5.00 for 8 rolls and 6 doughnuts. (2) Alfredo would have paid $10.00 if he had bought 16 rolls and 12 doughnuts.

题目翻译:在个面包店,每一个 R 花费 r,每一个 D 花费 d. 如果 A 买了 R 跟 D,A 买一个 R 花了多少钱? 仅条件一:8r+6t=5,无解,排除 A、D 仅条件二:16r+12t=10,无解,排除 B 一二同看:4r+3t=2.5,无解,排除 C 选择 E 难度评级:★

82 . 7746-!-item-!-187;#058&005794 Is x > 0 ? (1) xy > 0 (2) x + y > 0

题目翻译:RT 仅条件一:有两种情况,x、y 都小于 0,或者 x、y 都大于 0. 仅条件二:也有两种情况,都大于 0, 或者正数的绝对值大于负数的绝对值。 一二同看:条件 1 跟条件 2 有唯一交集“x、y 都大于 0”. 选 C 难度评级:★

83 . 7800-!-item-!-187;#058&005796 How much time did it take a certain car to travel 400 kilometers? (1) The car traveled the first 200 kilometers in 2.5 hours. (2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.

题目翻译:一个车开 400 公里要多长时间。 仅条件一:前 200 公里用了 2.5 小时 没有说车后 200km 也是原来的速度,所以错。 仅条件二: 如果这个车每小时多开 20 公里, 那么比原计划早 1 小时开完 400KM。400/x 400/(x+20) 可以,选 B 难度评级:★

-1

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84 . 7854-!-item-!-187;#058&005813 Each of the offices in a certain building has a floor area of 200, 300, or 350 square feet. How many offices are on the first floor of the building? (1) There is a total of 9,500 square feet of office floor space on the first floor of the building. (2) Ten of the offices on the first floor have floor areas of 350 square feet each.

题目翻译:一个楼里的一个办公室无非就是 200 300 或者 350 平米。问 1 楼有几个办公室 仅条件一:200x+300y+350z=9500 有很多解 仅条件二:Z=10 ,那么 200x+300y=6000 还是有很多解 一二同看:不用看了。 选 E 难度评级:★ Caution!:如果不会判断条件 1,那么可以这样想,连有一个确定值的条件 2 都不行,条件 1 就更不行了。

85 . 7908-!-item-!-187;#058&005852 Is n divisible by 12 ?

86 . 7962-!-item-!-187;#058&005867 Do more than 50 percent of the children in a certain group have brown hair? (1) 70 percent of the boys in the group have brown hair. (2) 30 percent of the children in the group are girls with brown hair.

题目翻译:有多于一半的孩子是棕色头发吗? 仅条件一:70%的男孩是棕头。男生的比例可能很低,也可能很高。所以单独不行 仅条件二:30%女孩是棕头。同上 一二同看:设男生 x 人,女生 y 人,那么(70%x+30%y)/x+y=30%+40%x/(x+y) 后半部分依 旧是不能确定 选 E 难度评级:★

87 . 8062-!-item-!-187;#058&006016 Is the integer n a multiple of 15 ? (1) n is a multiple of 20. (2) n + 6 is a multiple of 3.

题目翻译:N 这整数是 15 的倍数吗? 仅条件一:N 是 20 的倍数。 可以推出,N 可以整除 5 仅条件二:N+6 是 3 的倍数。 只有 3K+6 的形式才能被 3 整除,所以 N=3k 是 3 的倍数。 一二同看:N 即是 3 的倍数又是 5 的倍数,肯定被 15 整除。选 C 难度评级:★

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88 . 8117-!-item-!-187;#058&006040 If x + y ≠ 0, what is the value of (ax+ay)/(x+y) ? (1) x = 4 and y = 5. (2) a = 6

题目翻译:约分以后其实是求 a 的值 仅条件一:不充分,排除 A、D 仅条件二:充分,选择 B 难度评级:★

89 . 8171-!-item-!-187;#058&006095 What is the ratio of p to r ? (1) (2) The ratio of p to 3r is 5 to 9. The sum of p and r is 16.

题目翻译:p 与 r 的比值? 仅条件一:p/3r=5/9,则 p/r=5/3,满足。 仅条件二:不满足。故选 难度评级:★

90 . 8271-!-item-!-187;#058&006138 What is the value of a4 - b4 ? (1) a2 - b2 = 16 (2) a + b = 8

题目翻译:略 仅条件一:a4-b4=(a2+b2)(a2-b2),无法求出,不满足。 仅条件二:由(1) (2)可知,a-b=2,这样一来,a,b 都能求出,所以 a4-b4 也不在话下。 难度评级:★★★★ Caution:不要认为 a2+b2 的值求不出哦。

91 . 8325-!-item-!-187;#058&006143 In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant from the origin? (1) r + s = 1 (2) u = 1 - r and v = 1 - s.

题目翻译:在平面坐标轴中,点(r,s)和点(u,v)与原点距离相等吗? 仅条件一:连第 2 点都没提到,不满足。 仅条件二:易得 r=v,s=u,且 u+v=1,则说明这两点在直线 x+y-1=0 上且关于 x-y=0 的直线对 称,所以它们与原点距离相等,满足,故选 B。 难度评级:★★★
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92 . 8570-!-item-!-187;#058&006483 X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ? (1) X is a set of 5 consecutive odd integers, each less than 20. (2) Y is a set of 3 consecutive even integers, each less than 15.

题目翻译: x,y 是正整数集,x 集合中最大数是否大于 y 集合中最大数? 仅条件一:只提到 x,不满足。 仅条件二:只提到 y,不满足。 一二同看:当 X 为 19,18,17,16,15 时,19 肯定大于 Y 中最大数;但当 X 为 1,2,3, 4,5 时,就不一定了。故选 E。 难度评级:★
93 . 8624-!-item-!-187;#058&006485 The lifetimes of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m+ d ? (1) 68 percent of the distribution lies in the interval from m - d to m + d, inclusive. (2) 16 percent of the distribution is less than m - d.

题目翻译: 一个公司产的电池寿命平均值为 m,标准差为 d,有多少电池寿命长于 m+d? 仅条件一:无法判断。 仅条件二:更无法判断。 一二同看:可知大于 m+d 的有 1-68%-16%=16% 难度评级:★

94 . 8775-!-item-!-187;#058&006653 If |x + 2| = 4, what is the value of x ? (1) x2 ≠ 4 (2) x2 = 36

题目翻译: 略。 仅条件一:由提干可推到 x=2 或-6,由(1) ,则 x=-6,满足。 仅条件二:同理,x=-6,满足,故选 D。 难度评级:★

95 . 8829-!-item-!-187;#058&006700 If v and w are different integers, does v = 0 ? (1) vw= v2 (2) w = 2

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题目翻译: 如果 v 和 w 是不同整数,v 等于 0 吗? 仅条件一:可得 v=0 或 v=w,由提干排除 v=w,所以 v=0,满足。 仅条件二:推不出,选 A。 难度评级:★

96 . 8932-!-item-!-187;#058&006783 Is

( x ?5)

2

=5- x

(1) -x

x

>0

(2) 5 - x > 0

题目翻译:略。 仅条件一:提干要求 5>=x,(1)推出 x<0,不满足。 仅条件二:(2)推出 x<5,此时,原式恒成立,满足,故选 B。 难度评级:★★

97 . 8986-!-item-!-187;#058&006790 What is the median of a certain set of 7 numbers? (1) 3 of the numbers are less than 10. (2) 4 of the numbers are greater than 10.

题目翻译: 7 个数的中位数是多少? 仅条件一:显然推不出。 仅条件二:同上。 一二同看:只能推出中位数大于 10,选 E。 难度评级:★

98 . 9040-!-item-!-187;#058&006792 Is x + y < 1 ? (1) x < (2) y <
8 9 1 8

题目翻译:略。 仅条件一:缺少 y 的条件。 仅条件二:缺少 x 的条件。 一二同看:可推出 x+y<1+1/72,仍然可能大于 1,故选 E。 难度评级:★

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99 . 9094-!-item-!-187;#058&006821 For each home sold in County X, the buyer and the seller each must pay to County X a tax of 0.5 percent of the sale price of the home. Colleen recently sold her old home and bought a new home, both in County X. What was the total tax that Colleen paid to County X on these home sales? (1) (2) Colleen's old home had a sale price of $169,500. Colleen's new home had a sale price 20% greater than that of her old home.

题目翻译: 在 X 国,买家卖家都要交给国家房价 0.5% 的税。Colleen 最近卖了旧房买新房, 问他共交了多少税? 仅条件一:只知旧房要交的税。不满足。 仅条件二:什么都不知道,不满足。 一二同看:通过(1) (2) ,可求出新房要交的税。故选 C。 难度评级:★

100 . 9148-!-item-!-187;#058&006857 A certain bank charges a maintenance fee on a standard checking account each month that the balance falls below $1,000 at any time during the month. Did the bank charge a maintenance fee on Sue's standard checking account last month? (1) At the beginning of last month, Sue's account balance was $1,500. (2) During last month, a total of $2,000 was withdrawn from Sue's checking account.

题目翻译: 银行每个月对那些在月中任何时候余额小于 1000 元的帐号收管理费, 银行上个 月想苏收费了吗? 仅条件一:仅知道月初情况,不能保证之后情况,不满足。 仅条件二:只知道取走多少钱,余额不详,无法判断,不满足。 一二同看:没说存了多少钱,不满足,选 E。 难度评级:★★★ Caution!:别忘了有取就可能有存啊。

101 . 9205-!-item-!-187;#058&006882

In the figure above, lines l1 and l2 are parallel. What is the value of x ? (1) y = 87 (2) z = 93

题目翻译: 在上图中,直线 l1 和 l2 平行,x 为多少? 仅条件一:x 为 180-87=93,满足。
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仅条件二:x=z=93,满足。故选 D。 难度评级:★

102 . 9262-!-item-!-187;#058&006890

In the coordinate plane above, what is the area of rectangular region MNRS ? (1) M has coordinates (2, 1). (2) N has coordinates (2, 5).

题目翻译: 在上面的平面坐标系中,长方形 MNRS 面积多少? 仅条件一:求不出。 仅条件二:同上。 一二同看:只知道 MN=4,长不知道,无法求,故选 E。 难度评级:★

103 . 9889-!-item-!-187;#058&007222 How much did the taxi driver charge George for the trip to the airport? (1) George paid the taxi driver a tip equal to 15 percent of the amount the driver charged. (2) George paid the taxi driver a tip of $6.00.

题目翻译:出租车司机收了乔治多少钱? 仅条件一:只知道小费与车钱关系,不足以知道付的钱。 仅条件二:只知道小费,不足以知道付的钱。 一二同看:易算出车钱。故选 C。 难度评级:★

104 . 9943-!-item-!-187;#058&007224 A child selected a three-digit number, XYZ, where X, Y , and Z denote the digits of the number. If no two of the three digits were equal, what was the three-digit number? (1) The sum of the digits was 10. (2) X < Y < Z

题目翻译: 孩子选了个 3 位数 XYZ,XYZ 是不同的数字,这个三位数是什么? 仅条件一: X+Y+Z=10,不足以求出什么。不满足。 仅条件二:举例子。XYZ 可以是 127 或 136,无法确定。 一二同看:同(2)分析,故选 E。 难度评级:★

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105 . 9997-!-item-!-187;#058&007246 If b is positive, is ab positive? (1) a2b > 0 (2) a2 + b = 13

题目翻译:如果 b 是正数,ab 是正数吗? 仅条件一:只能推出 a 不等于 0.不满足。 仅条件二:a 仍然可能为负数。不满足。 一二同看:不满足,故选 E。 难度评级:★

106 . 10051-!-item-!-187;#058&007251 Robin split a total of $24,000 between two investments, X and Y . If investment Y earns 7 percent simple annual interest, how much of the total did Robin put into investment Y ? (1) Each investment earns the same dollar amount of interest annually. (2) Investment X earns 5 percent simple annual interest.

题目翻译:罗宾把 24000 元的投资分为 X,Y 两份,Y 投资年盈利 7%, 问 Y 投资金额多少? 仅条件一:不知 X 投资的年盈利率。不满足。 仅条件二:据题意可得 X(1+5%)=Y(1+7%)且 X+Y=24000,可且出 X 和 Y。故选 B. 难度评级:★

107 . 10578-!-item-!-187;#058&007600 Is 2x - 3y < x2 ? (1) 2x - 3y = -2 (2) x > 2 and y > 0.

题目翻译:略。 仅条件一: X2>0>-2,满足。 仅条件二:此时,X2-2X>0>-3Y,满足。故选 D。 难度评级:★

108 . 10635-!-item-!-187;#058&007601 If
x 2

=

3 y

, is x less than y ? 3 4

(1) y (2) y

? ?

题目翻译:略。 仅条件一: XY=6,可推得 0<X<=2<3<=Y,满足。
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仅条件二: XY=6,可推得 X>=3/2 或 X<0,无法比较 X,Y 大小。不满足。故选 A。 难度评级:★★

109 . 11067-!-item-!-187;#058&007824 Marta bought several pencils. If each pencil was either a 23-cent pencil or a 21-cent pencil, how many 23-cent pencils did Marta buy? (1) Marta bought a total of 6 pencils. (2) The total value of the pencils Marta bought was 130 cents.

题目翻译:玛塔买了些铅笔。铅笔要么是 23 分要么是 32 分钱,问玛塔买了多少 23 分的铅 笔? 仅条件一:知道买的铅笔总数不足以求出。不满足。 仅条件二:则有 23X+21Y=130,X,Y 分别为买 23 分铅笔与 21 分铅笔的数量。由于 X,Y 是整数,可推得 X=2,Y=4 且没有其它可能。故选 B。 难度评级:★★★★ Caution!:(2)中看似是 2 元一次方程,但别忘了 X,Y 是整数这一条件。

110 . 11121-!-item-!-187;#058&007826 If x and y are integers and x > 0, is y > 0 ? (1) 7x - 2y > 0 (2) -y < x

题目翻译:略。 仅条件一:y 可能正可能负,易举反例。不满足。 仅条件二:y 可能为 0 也可能为正为负。不满足。 一二同看:举反例,y=0,x 能满足条件;y=-1,x 仍能满足条件。故选 E。 难度评级:★

111 . 11229-!-item-!-187;#058&007982 A state legislature had a total of 96 members. The members who did not vote on a certain bill consisted of 25 who were absent and 3 who abstained. How many of those voting voted for the bill? (1) Exactly
1 3

of the total membership of the legislature voted against the bill.

(2) The number of Legislators who voted for the bill was 8 more than the total number who were absent or abstained.

题目翻译:某国的立法机关有 96 个成员,某次议案投票,有 25 个人缺席,3 个人弃权。求 投了多少赞成票? 仅条件一:仅有整体成员的 1/3 投了反对票。刨除反对票,缺席的和弃权的,可以求得赞成 票。保留 AD 仅条件二:投赞成票的是弃权和缺席人数的 8 倍。因为已知缺席和弃权人数, 可求得,答案
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D 难度评级:★

112 . 11432-!-item-!-187;#058&008149 If m and n are positive integers and mn = k, is m + n = k + 1 ? (1) m = 1 (2) k is a prime number.

题目翻译:如果 m 和 n 都是正整数且 mn=k,则 m + n = k + 1 ? 仅条件一:由 mn=k,m=1 推出 n=k,m + n = k + 1 成立。保留 AD 仅条件二:k 为质数,由 mn=k 推出 m 和 n 为 k 的因子,则 m=1,n=k 或者 m=k,n=1;等式成 立,答案 D 难度评级:★★ Caution!:将质数的因子与 mn=k 联系起来

113 . 11488-!-item-!-187;#058&008235 In a certain year the United Nations' total expenditures were $1.6 billion. Of this amount, 67.8 percent was paid by the 6 highest-contributing countries, and the balance was paid by the remaining 153 countries. Was Country X among the 6 highest-contributing countries? (1) 56 percent of the total expenditures was paid by the 4 highest-contributing countries, each of which paid more than Country X. (2) Country X paid 4.8 percent of the total expenditures.

题目翻译:联合国某年的总支出为 1.6b。其中,67.8%由 6 个贡献最大的国家支付,剩下的 由其他 153 个国家支付。 X 国在 6 个贡献最高的国家之中吗? 仅条件一:56% 部分由 4 个贡献最高的国家支付, 每个都比 X 国付的多。X 国可能在 6 个中 的 2 个中,也可能在剩余的 153 个国家中。不充分,排除 AD 仅条件二:X 国支付了 4.8%。已然不充分,无法判断。排除 B 一二同看:如果 X 国是 6 个国家中支付最少的,2X+56%=65.6%<67.8,仍然无法判断。答案 E 难度评级:★

114 . 11543-!-item-!-187;#058&008310 If
x? y z

=-2,is x positive?

(1) z is negative. (2) y is positive.
x? y z

题目翻译:

=-2,x 为正?

仅条件一:z 是负数。推出 x+y 为正数,无法得出 x 为正,排除 AD
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仅条件二:x=-2z-y,x 可以为正,也可以为负,排除 B 一二同看:依然无法判断 x 的正负,因为当 z=-1,y 为 1,x=1,当 z=-1,y=3 的时候,x=-1. 答案 E 难度评级:★

115 . 11595-!-item-!-187;#058&008332 List S and list T each contain 5 positive integers, and for each list the average (arithmetic mean) of the integers in the list is 40. If the integers 30, 40, and 50 are in both lists, is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T ? (1) The integer 25 is in list S. (2) The integer 45 is in list T.

题目翻译:S 数列和 T 数列各包含 5 个正整数, 每个数列的平均数是 40。如果整数 30,40,50 在两个数列中均存在,S 数列的标准差比 T 的标准差大吗? 仅条件一:由题干可知,5 个数中其中 3 个数的平均数为 40,可得剩下 2 个数的平均值也为 40,和为 80。S 中包含 25,则另外一个数为 55,由标准差的公式可知,这两个数偏离 40 的绝对值越大,标准差也就越大,因此只需判断这两个数与 40 的差的绝对值即可。仅条件 一无法判断 T 数列的情况,排除 AD 仅条件二:T 中的另外一个数为 80-45=35,无法判断数列 S 的情况,排除 B 2 2 一二同看: 条件一可知 (55-40) + (40-25)2=2*152; 条件二可知, (40-35) + (45-40)2=2*52, 不难判断 S 的标准差大于 T 的标准差。答案 C 难度评级:★★ Caution!:知道标准差的计算公式即不难判断

116 . 11649-!-item-!-187;#058&008377 On the number line, what is the distance between the point 2x and the point 3x ? (1) On the number line, the distance between the point -x and the point x is 16. (2) On the number line, the distance between the point x and the point 3x is 16.

题目翻译:数轴上,2x 与 3x 的距离有多远? 仅条件一:-x 与 x 的距离为 16。可求得 x 距离原点的距离为 8。3x 与 2x 的距离即为 x 的绝 对值,即为 8。保留 AD 仅条件二:x 与 3x 的距离为 2x 的绝对值,x 的绝对值可知为 8. 同样可解。答案为 D 难度评级:★

117 . 11703-!-item-!-187;#058&008423 What is the remainder when the positive integer n is divided by the positive integer k, where k > 1 ? (1) n = (k + 1)^3 (2) k = 5

题目翻译:正数 n 被正数 k 除的余数为多少,k>1?
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仅条件一:n=k3+ 3k2 +3k+1,前三项除 k 均能整除,因此余数为 1。保留 AD 仅条件二:k=5,余数可能是 1,2,3,4,无法判断,排除 BCDE,答案 A 难度评级:★

118 . 11804-!-item-!-187;#058&008456 Is x ? 3 ? (1) x2 – 9 = 0 (2) x < 10

题目翻译:不解释 仅条件一:可得出 x=3 或者 x=-3,排除 AD 仅条件二:x 可以等于 9,不满足条件,排除 BC 一二同看:x 可以等于-3,不满足条件,答案 E 难度评级:★

119 . 11954-!-item-!-187;#058&008495 At a two-candidate election for mayor, 3/4 of the registered voters cast ballots. How many registered voters cast ballots for the winning candidate? (1) 25,000 registered voters did not cast ballots in the election. (2) Of the registered voters who cast ballots, 55 percent cast ballots for the winning candidate.

题目翻译:两个候选人竞选市长,总选票数的 3/4 进行投票。获胜方获得的选票数为多少? 仅条件一:25000 张选票没有投票。总选票数为 25000*4,但是无法得知获胜方得多少票, 排除 AD 仅条件二:参与投票的选票中,55% 支持获胜方,不知道总票数为多少,排除 B 一二同看:由条件一可知参与投票的票数,由条件二可知道有 55% 的选票支持胜者,可求 解,答案 C 难度评级:★

120 . 12295-!-item-!-187;#058&008940 If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n ? (1) The greatest of the 6 consecutive integers is 20. (2) The average (arithmetic mean) of the 6 consecutive integers is 17.5.

题目翻译:n 是 6 个连续整数中的最大数与最小数的乘积,n 的值为多少? 仅条件一:最大数为 20,可知这 6 个连续整数为 15,16,17,18,19,20。n=15*20,保留 AD 仅条件二:6 个连续整数的平均数即为这 6 个数的中数,a3+a4=17.5*2,a4-a3=1;可以求出 第四个与第三个数,进而知道 6 个数各位多少,可求解。答案 D 难度评级:★

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121 . 12397-!-item-!-187;#058&009033 If n and s are each 2-digit positive integers, is n greater than s ? (1) The units digit of n is greater than the units digit of s. (2) The tens digit of n is greater than the tens digit of s.

题目翻译:n 和 s 均为两位正整数,n 大于 s? 仅条件一:n 的个位数比 s 的个位数大,不充分,排除 AD 仅条件二:n 的十位数比 s 的十位数大,充分,答案 B 难度评级:★ Caution!:只要最大的位数大,即可判断

122 . 12685-!-item-!-187;#058&009461 If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ? (1) 2 is not a factor of n. (2) 3 is not a factor of n.

题目翻译:如果 n 是个正整数, (n - 1)(n + 1)被 24 除后余数是 r,求 r 的值 仅条件一:2 不是 n 的因子,判断 n 为奇数,,n=2k+1, (n-1)(n+1) = (2k)(2k+2) ,连续偶数一 定某个被 2 整除,某个被 4 整除,无法判断余数。排除 AD 仅 条 件 二 : 3 不 是 n 的 因 子 , n=3y+1, (n-1)(n+1)=(3y)(3y+2) 或 者 n=3y+2, (n-1)(n+1)=(3y+1)(3y+3),均可被 3 整除,无法判断余数。排除 B 一二同看:既能被 3 整除,又能被 8 整除,一定可以整除 24,,余数为 0,答案 C 难度评级:★★ Caution!:一般想不到将 n 进行分解,比较耗费时间

123 . 12975-!-item-!-187;#058&009772 When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15 ? (1) n - 2 is divisible by 5. (2) t is divisible by 3.

题目翻译:正整数被 3 除余数为 2,正整数 t 被 5 除余数为 3,nt 被 15 除,余数为多少? 仅条件一:n-2 可被 5 整除。由题干得 n=3x+2,由条件一得 n-2=3x=5a,推得 x 为 5 的倍数, 设为 5b,则 n=15b+2。 无法判断 ,排除 AD 仅条件二:t=5y+3,t=3c,推出 y 是 3 的倍数,设为 3d,则 t=15d+3,仍然无法判断,排除 B 一二同看:nt=15*15bd+45b+30d+6,被 15 除后余数为 6,答案 C 难度评级:★★ Caution!:同样需要将 n 和 t 分解

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124 . 13029-!-item-!-187;#058&009789 A certain motel has a total of 540 units, each of which has a 1-person, 2-person, or 4-person capacity. How many people stayed in the motel's 4-person units yesterday? (1) At this motel,
1 3

of the units are 4-person units.

(2) Yesterday, 80 percent of the 4-person units in the motel were filled to capacity, and the rest of the 4-person units were empty.

题目翻译:某个旅馆一共有 540 间房间,每个房间可以容纳 1 人,2 人活着 4 人。昨天有多 少人住在 4 人的房间? 仅条件一:有 1/3 的房间是 4 人间,可知 4 人间的总数为 540/3=180,无法知道 4 人间住了 多少人。排除 AD 仅条件二:80%的 4 人间注满了人,其余的 4 人间空着,不知道四人间一共有多少,排除 B 一二同看:住的人数=180*80%*4 难度评级:★

125 . 13274-!-item-!-187;#058&009989 If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3@k? (1) 2 @ k = 3 (2) 1 @ 0 = k

题目翻译:如果@代表 2 个数学计算中的一个,加法或者乘法。如果 k 是整数,3@k 的值 是多少? 仅条件一:2@k=3,@只能是加法,k=1, 3@k=4,保留 AD 仅条件二:1@0=k,@可能为乘法,也可能为加法,排除 BCE,答案 A 难度评级:★

126 . 13661-!-item-!-187;#058&010116 If r and t are positive integers, is rt even? (1) r + t is odd. (2)

r

t

is odd.

题目翻译:如果 r 和 t 为正整数,rt 是偶数吗? 仅条件一:r+t 是奇数,则这两个数一个是奇数,一个是偶数,rt 为偶数,保留 AD 仅条件二:判断出 r 不可能为偶数,只能为奇数,无法判断 t 是奇数还是偶数, 排除 BDE, 答案 A 难度评级:★★ Caution!:几个数相乘,只要有一个为偶数,则乘积为偶数。

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127 . 13762-!-item-!-187;#058&010132 If 2/3 of the students at College C are business majors, what is the number of female students at College C ? (1)
2 5

of the male students at College C are business majors.

(2) 200 of the female students at College C are business majors.

题目翻译:如果 C 大学的 2/3 学生都是商科,有多少学生是女生? 仅条件一:2/3 的男学生是商科的,不知道男生与女生之间的数量关系,无法求解, 排除 AD 仅条件二:女生中有 200 人是学商科的,不知道其他学科的女生数量,排除 B 一二同看:2/3 的学生学商科, 2/3 的男生学商科,可知 2/3 的女生学商科,而又 200 个女 生学商科,易得女生人数为 300 人,答案 C 难度评级:★★

128 . 13817-!-item-!-187;#058&010140 Is y <
x? z 2

?

(1) y - x < z - y (2) z - y <
z?x 2

题目翻译:不解释 仅条件一:将右边的 y 移项,可得 2y<z+x,保留 AD 仅条件二:将不等式变形得 x+z<2y,y>(x+z)/2,能够判断 y 不是小于(x+z)/2,答案 D 难度评级:★★ Caution!: 这个题目的理解上有点问题, 题干的意思是是否能够用条件 1 和 2 判断 y 与(x+z)/2 的大小,而不是问条件 1 和 2 能否得出 y <
x? z 2

的结论。

129 . 13872-!-item-!-187;#058&010142 If t is a positive integer and r is the remainder when t 2 + 5t + 6 is divided by 7, what is the value of r ? (1) When t is divided by 7, the remainder is 6. (2) When t 2 is divided by 7, the remainder is 1.

题目翻译:如果 t 是一个正整数,r 是 t2 + 5t + 6 被 7 除之后的余数,求 r 的值? 仅条件一:t 被 7 除,余数为 6。t=7a+6,t2 + 5t + 6=49a2+119a+72,除 7 余数为 2,保留 AD 仅条件二:当 t 被 7 除之后的余数为 1,t =7b+1,t2 + 5t + 6=7b+6+ 7b ? 1 *5,无法知道
2 2

7b ? 1 被 7 除的余数,排除 BDE,答案 A
难度评级:★★

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130 . 14021-!-item-!-187;#058&010265 Set S consists of 20 different positive integers. How many of the integers in S are odd? (1) 10 of the integers in S are even. (2) 10 of the integers in S are multiples of 4.

题目翻译:S 数列包含有 20 个不同的正整数,数列 S 中有几个数是奇数? 仅条件一:S 中的 10 个整数是偶数,由于另外 10 个数不是偶数,则推出均为奇数,保留 AD 仅条件二:10 个整数是 4 的倍数,无法得出其他 10 个数是奇数还是偶数,排除 BCDE,答 案A 难度评级:★ Caution!:题目中的 different 是关键

131 . 14121-!-item-!-187;#058&010319 If w + x < 0, is w - y > 0 ? (1) x + y < 0 (2) y < x < w

题目翻译:不解释 仅条件一:假设 x=-3,y=-1,,w=-2,则 w-y=-1<0,排除 AD 仅条件二:直接可以推出 w - y > 0。答案 B 难度评级:★ Caution!:当无法判断的时候,果断使用假设验证

132 . 14175-!-item-!-187;#058&010326 If the drama club and music club are combined, what percent of the combined membership will be male? (1) Of the 16 members of the drama club, 15 are male. (2) Of the 20 members of the music club, 10 are male.

题目翻译:如果戏剧俱乐部和音乐俱乐部合并,男性占合并后的俱乐部人数的百分比是多 少? 仅条件一:16 个戏剧俱乐部成员中,15 名是男性。无法知道音乐俱乐部的男性数量,排除 AD 仅条件二:20 个音乐俱乐部成员中,10 名是男性。无法知道戏剧俱乐部的男性数量,排除 B 一二同看:无法知道有多少男性即参加了戏剧俱乐部又参加了音乐俱乐部,因此答案 E 难度评级:★★ Caution!:两个集合合并的情况下,要注意是否存在并集

133 . 14229-!-item-!-187;#058&010329 What is the average (arithmetic mean) height of the n people in a certain group?

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[?] [?]

134 . 14283-!-item-!-187;#058&010330 If m and n are integers, is m odd? [?] [?]

135 . 14337-!-item-!-187;#058&010335 How many more first-time jobless claims were filed in week P than in week T ? (1) For weeks P, Q, R, and S, the average (arithmetic mean) number of first-time jobless claims filed was 388,250. (2) For weeks Q, R, S, and T, the average (arithmetic mean) number of first-time jobless claims filed was 383,000.

题目翻译:不翻译 仅条件一:无解,排除 A、D 仅条件二:无解,排除 B 一二同看:因为其他三周都是 Q、R、S,所以第一个的总量比第二的总量多的就是 P 比 T 多的,有解,排除 E 选择 C 难度评级:★★

136 . 14393-!-item-!-187;#058&010357 x, 3, 1, 12, 8 If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers? (1) x > 6 (2) x is greater than the median of the 5 numbers.

题目翻译:x, 3, 1, 12, 8,中位数比平均值大吗? 仅条件一:x>6,若 x=7,中位数是 7,均值是 6.2,大于;若 x 大于等于 8,中位数是 8, 均值最小是 6.4,6.6,6.8,7,7.2,但随着 x 不断增大均值总会超过 8。不充分,排除 A、 D 仅条件二:x 比 5 个数的中位数大,说明 x 最小是 9, 此时均值是 6.6,但随着 x 不断增大均 值总会超过 8。不充分,排除 B 一二同看:分析同仅条件二 难度评级:★★★

137 . 14447-!-item-!-187;#058&010361 If x and y are positive integers, is xy a multiple of 8 ?

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(1) The greatest common divisor of x and y is 10. (2) The least common multiple of x and y is 100.

题目翻译:不翻译 仅条件一:x 和 y 的最大公约数是 10,只能保证 xy 可以被 4 整除(例:30、50) ,不充分, 排除 A、D 仅条件二:x 和 y 的最小公倍数是 100, 也只能保证 xy 可以被 4 整除(例:4、25) , 不充分, 排除 B 一二同看:两数的最大公约数是 10,说明两数都是 10 的倍数,最小公倍数又是 100,只可 能是 20 和 50,充分,排除 E 选择 C 难度评级:★★★★

138 . 14501-!-item-!-187;#058&010393 If zy < xy < 0, is |x - z | + |x | = |z | ? (1) z < x (2) y > 0

题目翻译:不翻译 仅条件一:z<x 可推出 y 为正数且 z<x<0,|x - z | + |x | =x – z – x = -z = |z |,充分,保留 A、 D 仅条件二:同上,排除 A 选择 D 难度评级:★★★

139 . 14556-!-item-!-187;#058&010396 If machine J, working alone at its constant rate, takes 2 minutes to wrap 60 pieces of candy, how many minutes does it take machine K, working alone at its constant rate, to wrap 120 pieces of candy? (1) Machine K, working alone at its constant rate, takes more than 5 minutes to wrap 60 pieces of candy. (2) Machines J and K, working together at their respective constant rates, take 1 minute and 30 seconds to wrap 60 pieces of candy.

题目翻译:J2 分钟可以包 60 块糖,K 需要多久可以包 120 块糖呢? 仅条件一:K 包 60 块糖需要超过 5 分钟的时间,不充分,排除 A、D 仅条件二:J 和 K 一起需要 1 分 30 秒包 60 块糖,用效率相加的公式可以求出 K 的情况, 充分,选择 B 难度评级:★

140 . 14610-!-item-!-187;#058&010398 A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more video cameras in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video cameras did the manufacturer produce in 1995 ? [?]

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[?]

141 . 14664-!-item-!-187;#058&010407 Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people? (1) Of the 20 people, 10 used only 1 ticket. (2) Of the 20 people, 4 used neither ticket.

题目翻译:20 个人,每个人买了 2 张演唱会的票,有些 2 张都用了,有些用了 1 张,有些 1 张都没用。20 个人买的票有多少被用掉了呢? 仅条件一: 20 个人里有 10 个人用了一张票, 但不知道有多少人用了 2 张票有多少人没有用, 故不充分,排除 A、D 仅条件二:20 个人里有 4 个人没有用票,但不知道有多少人用了 2 张票有多少用了一张票, 不充分,排除 B 一二同看:充分,排除 E 选择 C 难度评级:★

142 . 14718-!-item-!-187;#058&010409 At a certain stand, all soft drinks cost the same and all sandwiches cost the same. How much does 1 sandwich cost at the stand? (1) At the stand, 1 sandwich and 2 soft drinks cost a total of $3.15. (2) At the stand, 3 sandwiches and 1 soft drink cost a total of $5.70.

题目翻译:在一个特定的标准下,所有的软饮料价格一样,所有的三明治价格一样。一块三 明治多少钱? 仅条件一:1s+2d=3.15,无解,排除 A、D 仅条件二:3s+d=5.7,无解,排除 B 一二同看:联立可求解,排除 E 选择 C 难度评级:★

143 . 14772-!-item-!-187;#058&010415 If K is a positive three-digit integer, what is the hundreds digit of K ? (1) The hundreds digit of K + 150 is 4. (2) The tens digit of K + 25 is 7.

题目翻译:K 是一个正的三位数,百位是多少? 仅条件一:K+150 的百位是 4,不充分(270,330) ,排除 A、D 仅条件二:K+25 的十位是 7,不充分(250,450) ,排除 B 一二同看:K+25 的十位是 7,K 的十位是 4 或 5,K+150 的百位是 4,仍然不充分(250, 340) ,排除 C 选择 E
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难度评级:★★★

144 . 14826-!-item-!-187;#058&010416 In the xy-plane, point P has coordinates (a, b) and point Q has coordinates (c, d). What is the distance between P and Q ? (1) b - d = 4 (2) a - c = 3

题目翻译:点 P 坐标(a,b),点 Q 坐标(c,d),求 PQ 之间的距离。 仅条件一:不充分,排除 A、D 仅条件二:不充分,排除 B 一二同看:代入公式可得|PQ|=5,排除 E 选择 C 难度评级:★★

145 . 14880-!-item-!-187;#058&010418 If a, b, and c are positive integers, is b between a and c ? (1) b is 3 greater than a, and b is 5 less than c. (2) c is 5 greater than b, and c is 8 greater than a.

题目翻译:若 a,b,c 都是正整数,那么 b 是否处于 a 和 c 之间? 仅条件一:∵b-3=a ∴b>a 又∵b+5=c ∴b<c 因此 a<b<c 充分,保留 A、D 仅条件二:∵c-5=b ∴c>b 又 c-8=a ∴b+5=a+8 ∴b>a 因此 c>b>a,充分,排除 A 选择 D 难度评级:★★

146 . 14980-!-item-!-187;#058&010478 At a certain refreshment stand, all hot dogs have the same price and all sodas have the same price. What is the total price of 3 hot dogs and 2 sodas at the refreshment stand? (1) The total price of 5 sodas at the stand is less than the total price of 2 hot dogs. (2) The total price of 9 hot dogs and 6 sodas at the stand is $21.

题目翻译:路边摊上所有的热狗都是一个价,所有的汽水都是一个价,那么 3 只热狗和 2 杯汽水多少钱? 仅条件一:5s<2h 不充分,排除 A、D 仅条件二:9h+6s=21 等式两边同时除以 3,得 3h+2s=7,充分,选择 B 难度评级:★

147 . 15034-!-item-!-187;#058&010480 If a certain company purchased computers at $2,000 each and printers at $300 each, how many computers did it purchase? (1) More than three printers were purchased.

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(2) The total amount for the purchase of the computers and the printers was $15,000.

题目翻译:某公司购买单价为$2,000 的电脑和单价为$300 的打印机,问公司买了多少台电 脑? 仅条件一:p>3 不充分,排除 A、D 仅条件二: $15,000=$2,000*c+$300*p ∵c、 p 都是正整数, ∴只有一组解 c=6,p=10 充分, 选择 B 难度评级:★★

148 . 15274-!-item-!-187;#058&010713 If x = 3 and y = 6, is y > nx + k ? (1) n = 5 (2) k=-10

题目翻译:不翻译 仅条件一:不知道 k,不充分,排除 A、D 仅条件二:不知道 n,不充分,排除 B 一二同看:可求解,排除 E 选择 C 难度评级:★

149 . 15328-!-item-!-187;#058&010715 Does x + c = y + c ? (1) x = y (2) x = c

题目翻译:不翻译 仅条件一:充分,保留 A、D 仅条件二:不充分,排除 D 选择 A 难度评级:★

150 . 15382-!-item-!-187;#058&010719 If n is an integer between 3 and 9, what is the value of n ? (1) On the number line, the distance from 3 to n is 2/3 of the distance from 3 to 9. (2) On the number line, n is 10 units to the right of -3.

题目翻译:如果 n 在 3-9 之间,n 是多少? 仅条件一:可设其中一距离为 x,可求解,充分,保留 A、D 仅条件二:n 在-3 右边 10 个单位,充分,排除 A 选择 D 难度评级:★

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151 . 15486-!-item-!-187;#058&010743 Is the average (arithmetic mean) of 5 different positive integers at least 30 ? (1) Each of the integers is a multiple of 10. (2) The sum of the 5 integers is 160.

题目翻译:5 个不相等的正整数之和的算术平均数是否至少是 30 仅条件一:每个数都是 10 的倍数且不相等,则最小数的组合是 10,20,30,40,50,其算 术平均数为 30,充分,保留 A、D 仅条件二:5 个数之和是 160,算术平均数=160/5=32>30,充分,排除 A 选择 D 难度评级:★★

152 . 15540-!-item-!-187;#058&010751 A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white? [?] [?]

153 . 15687-!-item-!-187;#058&010776 On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first x miles? (1) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles. (2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance.

题目翻译:J 开车从 A 市到 B 市,前 x 英里他的速度是 50 英里每小时,剩余路程中他的速 度是 60 英里每小时。J 花了多久开完了前 x 英里? 仅条件一:x+y=530,x/50+y/60=10 解得 x=350,y=180,充分,保留 A、D 仅条件二:x/50-4=y/60,不充分,排除 D 选择 A 难度评级:★★

154 . 15741-!-item-!-187;#058&010784 To install cable television in a home, a certain cable company charges a basic fee of $30 plus a fee of $20 for each cable outlet installed in the home. How much did the cable company charge the Horace family for installing cable television in their home? (1) The cable company installed three cable outlets in the Horace family home. (2) The amount that the cable company charged the Horace family for installing cable television in their home was equivalent to an average (arithmetic mean) charge of $30 per cable outlet installed.

题目翻译:给家里装有线电视,某有线电视公司的收费标准是基准$30 另加每个有线接口 $20,那么这家公司给 H 家安装有线电视时收了他家多少钱? 仅条件一:total=$30+$20*3=$90,充分,保留 A、D
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仅条件二:设接口数为 n,$30+$20*n=$30*n,n=3,充分,排除 A 选择 D 难度评级:★★

155 . 15795-!-item-!-187;#058&010817 If 500 is the multiple of 100 that is closest to x and 400 is the multiple of 100 that is closest to y, which multiple of 100 is closest to x + y? (1) x < 500 (2) y < 400

题目翻译:在 100 的倍数中,500 离 x 最近,400 离 y 最近,那么 100 的那个倍数离 x +y 最 近呢? 仅条件一:根据题意,知道 450 < x < 550,350 < y < 450,根据条件一:x < 500,800 < x + y < 950,无法确定,比如说 x +y=850,离 800,和 900 的距离相同。所以排除 A、D。 仅条件二:根据条件二:y < 400,800 < x + y < 950,和条件一一样,无法确定。排除 B。 一二同看:450 < x < 500, 350 < y < 400,则 800<x +y<900,同样无法确定,因为当 800<x +y<850 时,最近的是 800,当 850<x +y<900,则是 900,所以选 E。 难度评级:★★★ Caution!:重点理解 500 is the multiple of 100 that is closest to x 的含义.

156 . 15849-!-item-!-187;#058&010825 Each of the numbers w, x, y, and z is equal to either 0 or 1. What is the value of w + x + y + z ? [?] [?]

157 . 15904-!-item-!-187;#058&010840 A certain list consists of five different integers. Is the average (arithmetic mean) of the two greatest integers in the list greater than 70? (1) The median of the integers in the list is 70. (2) The average of the integers in the list is 70.

题目翻译: 一个列中包含5个不同的整数,两个最大的整数的平均数大于70吗? 仅条件一:这个列整数的中位数为70.知道第三个为70, 因为每个整数不同,所以第四 和第五个数肯定大于70,所以两个最大的整数的平均数大于70。保留 A、D。 仅条件二:这个列整数的平均数为70.这5个数的平均为70,必然两个最大的整数的平 均数大于70。排除 A,选择 D。 难度评级:★★

158 . 15958-!-item-!-187;#058&010868 A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the store's gross profit on the 20 coats?

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(1) If the selling price per coat had been twice as much, the store's gross profit on the 20 coats would have been $2,400. (2) If the selling price per coat had been $2 more, the store's gross profit on the 20 coats would have been $440.

题目翻译: 一个商店购买20件外套,每件花费相同的钱,然后这20件外套都以同样的 价格卖出。此商店这20件外套的净利润为多少? 仅条件一:如果每件外套的卖价变为了两倍,这个商店的净利润成为2400。设每个 coat 售价为 S 成本为 C。 (2S-C)× 20=2400,但无法求(S-C)× 20。所以无解,排除 A、D。 仅条件二:如果每件卖价增加2,商店的净利润将会为440。(s+2-c)× 20=440,可求出 (s-c)× 20=400。选择 B。 难度评级:★★

159 . 16012-!-item-!-187;#058&010902 Beth and Jim each received a salary increase. If Jim's salary was increased by the same percent as Beth's salary, did Beth receive a greater dollar increase in salary than Jim? (1) Before the increases, Jim’s salary was greater than $25,000. (2) Before the increases, Jim’s salary was 4/5 of Beth’s salary.

题目翻译:B 和 J 各收到了一份薪金的增长,如果两人的增幅一样,B 的增量比 J 多吗? 仅条件一:不知道两者谁多谁少,不充分,排除 A、D。 仅条件二:知道两者谁多谁少,充分,选择 B。 难度评级:★

160 . 16066-!-item-!-187;#058&010935 All the clients that Company X had at the beginning of last year remained with the company for the whole year. If Company X acquired new clients during the year, what was the ratio of the number of clients that Company X had at the end of last year to the number of clients that it had at the beginning of last year? (1) The ratio of the number of clients that Company X had at the beginning of last year to the number of new clients that it acquired during the year was 12 to 1. (2) Company X had 144 clients at the beginning of last year.

题目翻译: 公司X在去年最开始有的客户在整个一年中都保留在此公司内。如果公司X在 一年中取得了新的客户,公司X去年底的客户数量与在年初的客户数量的比例是多少? 仅条件一: 公司X去年年初的客户数与它在一年中获得的客户数量的比例是12/1。 可以 得出公司X去年底的客户数量与在年初的客户数量的比例是 13 to 12。有解,保留 A、D。 仅条件二:公司X在去年年初有144个客户。无法知道在一年中增加了多少人,去年年底 共有多少人。所以无解,排除 D,选择 A。 难度评级:★★

161 . 16120-!-item-!-187;#058&010949 In the xy-coordinate plane, line m and line k intersect at the point (4, 3). Is the product of their slopes negative?

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(1) The product of the x-intercepts of lines m and k is positive. (2) The product of the y-intercepts of lines m and k is negative.

题目翻译:xy 平面,线m,k交于点(4,3)。他们的斜率的乘积是负数吗? 仅条件一:若已知两直线与 X 轴交点乘积为正,则两直线斜率可能均为正,均为负,或一正 一负。无法确定,排除 A、D。 仅条件二:已知两直线交点与 Y 轴交点乘积为负,则两直线斜率可能皆为正或一正一负。 无法确定。排除 B。 一二同看:条件一,二组合,则可知两直线斜率为一正一负。确定,则选C。 难度评级:★★★

162 . 16220-!-item-!-187;#058&011014 If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r ? (1) n is odd. (2) n is not divisible by 8.

题目翻译:r 是(n^2-1)被 8 除时的余数,r 的值是多少 仅条件一:n 是奇数,n^2-1=(n+1)(n-1),因为 n 是奇数,所以 n+1 和 n-1 是连续偶数,连续 偶数必然一个可以被 2 整除,另一个可以被 4 整除,故被 8 整除余数为 0,充分,保留 A、 D 仅条件二:n 不可以被 8 整除,不充分,排除 D 选择 A 难度评级:★★★

163 . 16419-!-item-!-187;#058&011075 In a certain election, 240 men and 280 women voted for the winning candidate. What was the total number of men and women who voted in the election? [?] [?]

164 . 16473-!-item-!-187;#058&011078 If m v < p v < 0, is v > 0 (1) m < p (2) m < 0

题目翻译:如果 m v < p v < 0 ,v>0 吗? 仅条件一:当m<p 时,v>0,可确定,保留 A、D。 仅条件二:当 m < 0,因为 m v< 0,所以v>0。可确定,排除 A,选择 D。 难度评级:★

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165 . 16527-!-item-!-187;#058&011081 If x and y are points on the number line, what is the value of x + y ? (1) 6 is halfway between x and y. (2) y = 2x

题目翻译: x, y 是在数轴上的点,x +y 的值是多少? 仅条件一:6 在 x, y 的中间。X +y=12。可解,保留 A、D。 仅条件二:y = 2x,无法求出 x +y。不可解,排除 D,选择 A。 难度评级:★

166 . 16673-!-item-!-187;#058&011115 If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p^2t ? (1) m has more than 9 positive factors. (2) m is a multiple of p3.

题目翻译:如果 p 和 t 是 m 仅有的质因子,m 是 p^2*t 的倍数吗? 仅条件一:m 有超过 9 个正因子,有可能 m 只含一个 p,不充分,排除 A、D 仅条件二:m 是 p^3 的倍数,且 m 又至少含有一个 t,充分,选择 B 难度评级:★★

167 . 16727-!-item-!-187;#058&011198 A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area? (1) The distance between point P and point X is 4.5. (2) The distance between point X and point Y is 9.

题目翻译: 一个圆形面积的中心在P点,半径是4,点X,Y在此圆形区域的同一平面。 点Y位于圆形区域的外面吗? 仅条件一:点P,X的距离是 4.5。不知道 p 到 y 的距离,无法确定,排除 A、D。 仅条件二:点X,Y的距离是 9。不知道 p 跟 x 和 p 跟 y 的距离,无法确定,排除 B。 一二同看:结合在一起,可确定在圆形区域外面。所以选C。 难度评级:★

168 . 16781-!-item-!-187;#058&011242 In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the senior class are male? (1) There are 840 students in the senior class. (2) 75 percent of the students in the senior class have applied to college.

题目翻译: 一个班级, 72% 的男生和 80% 的女生已经申请了大学。 此班级男生的比例是多少? 仅条件一:有 840 名学生。M+F=840,无法求出F/( M+F)。排除 A、D。
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仅条件二:75%的学生已经申请了上大学。75%( M+F)=72%M+80%F,可以求出F/( M+F)。 选择 B。 难度评级:★★

169 . 16835-!-item-!-187;#058&011243 Greta and Randy collected bottles to be recycled. How many bottles did Randy collect? (1) Greta and Randy collected a total of 85 bottles. (2) Greta collected 15 more bottles than Randy did.

题目翻译: Greta and Randy 收集一些瓶子, 这些瓶子将会被回收。 Randy 收集了多少瓶子? 仅条件一:两人共收集了85个。假设分别收集x,y。则 x +y=85,无法求出x。排除 A、 D。 仅条件二:Greta 比 Randy 多收集了15个瓶子,x-y=15,仍无法求出 x。排除 B。 一二同看:两个方程组,可求出 x, y 的值。所以选择D。 难度评级:★

170 . 16889-!-item-!-187;#058&011265 If z t < -3, is z < 4 ? (1) z < 9 (2) t < -4

题目翻译: 如果 zt < -3,z < 4 吗? 仅条件一:当 z<9 时,假设 z=8,t=-1 代入 z t < -3 为-24 < -3,因此不可得知 z < 4 是否成立。 排除 A、D。 仅条件二:当 t < -4 时,假设 t=-5,z=8 代入 z t < -3 为-40 < -3,因此不可得知 z < 4 是否成立。 排除 B。 一二同看:条件一,二均满足时。假设 t=-5,z=8 代入 z t < -3 为-40 < -3,因此不可得知 z < 4 是否成立。选择E。 难度评级:★★★

171 . 16943-!-item-!-187;#058&011304 If k is a positive integer and the tens digit of k + 5 is 4, what is the tens digit of k ? (1) k > 35 (2) The units digit of k is greater than 5.

题目翻译:如果 k 是一个正整数,且 k + 5 的十位是 4,那么 k 的十位上的数是什么? 仅条件一:k > 35,如 k 可为 36,41…所以无法确定,排除 A、D。 仅条件二:k 的个位上的数大于5,那么 k 的十位上的数肯定为3。选择 B。 难度评级:★★

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172 . 17043-!-item-!-187;#058&011315 If a and b are nonzero numbers on the number line, is 0 between a and b ? (1) The distance between 0 and a is greater than the distance between 0 and b. (2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum a + b .

题目翻译: 如果 a,b 是数轴上的非零数字,问0在 a, b 之间吗? 仅条件一:0 与 a 的距离大于 0 与 b 之间的距离。|a|>|b|,无法确定,排除 A、D。 仅条件二: 0 与 a 的距离和 0 与 b 之间的距离的和要比 0 与 a +b 的距离大。|a|+|b|>|a +b| 有当 a,b 异号时才符合条件。 难度评级:★★ Caution!:即公式|a|+|b|>|a +b| 只有当 a, b 异号时才符合条件。



173 . 17097-!-item-!-187;#058&011316 In the xy-plane, line k passes through the point (1,1) and line m passes through the point (1,-1). Are lines k and m perpendicular to each other? (1) Lines k and m intersect at the point (1,-1). (2) Line k intersects the x-axis at the point (1,0).

题目翻译: 在 x y 平面,线 k 过点(1,1),线 m 过点(1,-1)。线 k,m 互相垂直吗? 仅条件一:线 k, m 交于点(1,-1)。可求出 k 斜率,但无法求出 m 的斜率。排除 A、D。 仅条件二:线 k 与 x 轴交于点(1,0)。可求出 k 斜率,但无法求出 m 的斜率。排除 B。 一二同看:条件一,二结合,仍旧无法求出 m 的斜率,所以选择E。 难度评级:★★

174 . 17151-!-item-!-187;#058&011360 Each week Connie receives a base salary of $500, plus a 20 percent commission on the total amount of her sales that week in excess of $1,500. What was the total amount of Connie's sales last week? (1) Last week Connie's base salary and commission totaled $1,200. (2) Last week Connie's commission was $700.

题目翻译: 上个星期,Connie 收到基本工资$500,加上她的销售超过 1500 部分的 20% 的 commission,Connie 上个星期总共的销售是多少? 仅条件一:设总金额为 x 元,则根据条件,500+(x-1500)× 20%=1200,x=5000。保留 A、D。 仅条件二:(x-1500)× 20%=700,x=5000。排除 A,选择 D。 难度评级:★

175 . 17205-!-item-!-187;#058&011383 Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that Ann bought was twice the number of oranges and if the number of pears that Ann bought was the same as the number of apples and oranges combined, what fraction of the total number of pieces of fruit that Ann bought were

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pears? (1) Ann bought a total of 18 pieces of fruit. (2) Ann bought 5 bananas.

题目翻译: Ann 卖了五种不同的水果:apples, oranges, pears, mangoes, and bananas。 如果 apple 数量是 orange 的两倍,pear 数量是 apple 和 orange 数量的总和,pear 占的比重是多少? 仅条件一:设 apples 数量有 a, oranges 数量有 o, pears 数量有 p, mangoes 数量有 m, bananas 数量有 b,则根据题目知道:a=2o,p=a +o。共买了 18 个水果,a +o +p+m+b=18,无法求 出。排除 A、D。 仅条件二:买了5个 bananas.仍不知其他水果的数量情况。无法求出。排除 B。 一二同看:已知的数据代入方程中,仍无法求出。所以选E。 难度评级:★★

176 . 17259-!-item-!-187;#058&011402 In 1995 Division A of Company X had 4,850 customers. If there were 86 service errors in Division A that year, what was the service-error rate, in number of service errors per 100 customers, for Division B of Company X in 1995 ? (1) In 1995 the overall service-error rate for Divisions A and B combined was 1.5 service errors per 100 customers. (2) In 1995 Division B had 9,350 customers, none of whom were customers of Division A.

题目翻译:在 1995 年,公司X的机构A有 4850 名客户,如果在那一年在机构A中有 86 个 服务错误,那么在 1995 年,机构B的服务错误率是多少? 仅条件一 :设机构B服务的人数是M,服务错误的数量是N,则根据条件一, (86+N)/(4850+M)=1.5/100,无法求出。排除 A、D。 仅条件二:只知道M是 9350,仍无法求出。排除 B。 一二同看:两个条件相结合,可求出M,N。所以选C。 难度评级:★

177 . 17313-!-item-!-187;#058&011410 If x and y are positive integers, is x an even integer? (1) x (y + 5) is an even integer. (2) 6y 2+ 41y + 25 is an even integer.

答案:E 题目翻译:X,Y 均为正整数,X 是偶数吗? 仅条件一:x or (y+5) or both can be even,无法判定,排除 A,D 仅条件二:(y+5)(6y+5)+6y = even integer,( y+5)(6y+5) = even integer (y+5) or (6y+5) is even. y = 5 排除 B 一二同看:无法判定,排除 C,选择 E 难度评级:★★★★★

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178 . 17370-!-item-!-187;#058&011434

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the deg ree measure of angle ∠ BAO ? (1) The degree measure of angle COD is 60. (2) The degree measure of angle BCO is 40.

答案:D 题目翻译:如图所示,点 O 为半圆的重点,点 B,C,D 在半圆上,如果 AB=OC,∠BAO 为 多少°? 仅条件一: ?BCO ? ?BAO ? 60 , ?BCO ? 2x ?BAO , 3x ?BAO =60, ?BAO =20,保留 A,D 仅条件二: ?BCO ? 2x ?BAO =40, ?BAO =20,排除 A,选择 D。 难度评级:★★★★★

179 . 17563-!-item-!-187;#058&011544 Working independently at their respective constant rates, pumps X and Y took 48 minutes to fill an empty tank with water. What fraction of the water in the full tank came from pump X ? (1) Working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water. (2) Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank with water.

答案:D 题目翻译:独立工作的泵 X,Y,花 48 分钟将罐里注满水,这个注满水的罐,有多少水来自 泵 X? 仅条件一: 仅条件二:
1 80
1

x48=
?

4 5

,保留 A,D A,选择 D

x

1 1 ? , x=80,排除 120 48

难度评级:★★

180 . 17617-!-item-!-187;#058&011567 What is the value of v 3 - k3 ? (1) vk > 0 (2) v - k = 6

答案:E 题目翻译:v3 - k3 的值是多少? 仅条件一 : 两个未知,排除 A,D
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(v ? k )3 ? v 3 ? 2v 2k ? 2vk 2 ? k 3



v 3 - k 3 = (v ? k )3 + 2v 2k - 2vk 2 =216+ 2v 2k - 2vk 2 =216+2vk(v-k),排除 B

一二同看:still don’t know v and k, 排除 C,选择 E 难度评级:★★★★

181 . 17723-!-item-!-187;#058&011591 Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out buy? (1) Rasheed bought 1 fewer package of chocolate bars than toffee bars. (2) Rasheed handed out the same number of each kind of candy bar.
2 3

of the chocolate bars and

3 5

of the toffee bars. How many packages of chocolate bars did Rasheed

答案:C 题目翻译:R 买了两种糖果,巧克力和奶糖,每包有两个糖果。他发放了 2/3 的巧克力糖, 3/5 的奶糖,他一共买了多少包巧克力糖? 仅条件一:设 x 为 chocolate 的数量,y 为 toffe 的数量, x-2 = y ,条件不足,排除 A,D
2 3 x ? y 3 5 仅条件二:

,不充分,排除 B 一二同看:两式联立解(x/2) ,排除 E,选择 C 难度评级:★★★

182 . 17777-!-item-!-187;#058&011599 If m and r are two numbers on a number line, what is the value of r ? (1) The distance between r and 0 is 3 times the distance between m and 0 . (2) 12 is halfway between m and r.

答案:E 题目翻译:m 和 r 是一个数列中的两个数,r 值为多少? 仅条件一:|r|=3|m| r = 3m or -3m,不充分,排除 A,D 仅条件二:m+r = 24,仍不充分,排除 B 一二同看: m+3m=24, m=6, r=18, m-3m=24, m=-12, r=36 (not able to decide r’s value), 排除 C, 选择 E 难度评级:★★★

183 . 17831-!-item-!-187;#058&011633 If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers? (1) m is not divisible by 3.

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(2) m is not divisible by 5.

答案:A 题目翻译:m 是一个 2 到 30 之间的奇数,m 有多少个不同的质因子? 仅条件一:2<m<30 {3,5,7,9,11,13,15,17,19,21,23,25,27,29} ,m excludes {3,6,9,12,15,18,21,24,27}={5,7,11,13,17,19,23,25,29} 全部只可以被自己和 1 除,保留 A,D 仅条件二:m excludes {5,10,15,20,25}={3,7,9,11,13,17,19,21,23,27,29} 21 除了自己和 1 还可以被 7 除,排除 D,选择 A 难度评级:★★★★★

184 . 17933-!-item-!-187;#058&011666 If k is an integer greater than 1, is k equal to 2r for some positive integer r ? (1) k is divisible by 26. (2) k is not divisible by any odd integer greater than 1.

答案:B 题目翻译:K 是大于 1 的整数,如果 r 为正整数,K= 2r 吗? 仅条件一: k/(2^6)=整数(设 X) 所以 k=(2^6)X 当 X 等于 2 的倍数 则条件成立 反之不成立 因此 条件一不充分 ,排除 A,D 仅条件二: K 不能被大于一的任何奇数整除 换句话说 K 只能被 2 的倍数整除 也就是说 K 一定是 2 的倍数且只有 1 和 2 的因子 所以条件 2 充分,选择 B 难度评级:★★★★

185 . 17987-!-item-!-187;#058&011677 Of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the members speak only Spanish. If no member speaks all three languages, how many of the members speak two of the three languages? (1) 60 of the members speak only English. (2) 20 of the members do not speak any of the three languages.

答案:C 题目翻译:一个协会有 200 名会员,会说德语的也会说英语,70 个人只会说西班牙语,如 果没有人三种语言都会,有多少人能说两种语言? 仅条件一:依题意,会至少两种语言的会员是:全部 – (只会英文) – (只会西班牙文) – (3 种都不会),不知道 3 种都不会的,所以不充分,排除 A,D 仅条件二:不知道只会英文的,排除 B
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一二同看:代入以上算式可以得知。排除 E,选择 C 难度评级:★★★★

186 . 18041-!-item-!-187;#058&011685 If a, b, and c are integers, what is the value of a ? (1) (a - 7)(b - 7)(c - 7) = 0 (2) bc = 18

答案:C 题目翻译:a,b,c 都是整数,a 的值为多少? 仅条件一:b 或 c 是 7,a 可以是任何数,排除 A,D 仅条件二:没有与 a 有关的条件,不能判断 a 值,排除 B 一二同看:bc 不能被 7 除,b 或 c 都不可能 7 ,只有 a 是 7 才能符合条件(1)&(2) ,排除 E , 选择 C 难度评级:★★★

187 . 18095-!-item-!-187;#058&011720 An antique dealer bought a coffee table that was then sold for a profit. What was the selling price of the coffee table? (1) The dealer's cost for the coffee table was $340. (2) The dealer's gross profit on the coffee table was 15% of the selling price.

答案:C 题目翻译:一个股东经销商买了一个咖啡桌,之后再售出获利。咖啡桌的卖价是多少? 仅条件一:不知道利润,排除 A,D 仅条件二:不知道成本,排除 B 一二同看:设 p 为售价, p = 0.15p+340 ,充分,排除 E ,选择 C 难度评级:★★★

188 . 18293-!-item-!-187;#058&011863 Is x4 + y 4 > z4 ? (1) x2 + y 2 > z2 (2) x + y > z

答案:E 2 2 2= 4 2 2 4 4 仅条件一: (x + y ) x +2x y +y > z ( 不能得知),排除 A,D 4= 4 3 2 4 4 仅条件二: (x+y) x +4x y +?.+y > z ( 不能得知),排除 B 一二同看:仍然无法推断,排除 C ,选择 E 难度评级:★★★★

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189 . 18439-!-item-!-187;#058&011934 In the xy-plane, the line k passes through the origin and through the point (a,b), where ab (1) The slope of line k is negative. (2) a < b

?

0. Is b positive?

答案:C 题目翻译:XY 平面,K 线穿过原点和点(a,b), 且 ab ? 0 。B 为正吗? 仅条件一:直线通过 II,IV 象限. (a,b)=(-,+) or (+,-),不充分,排除 A,D 仅条件二:不能判断 b 的正负值,排除 B 一二同看: (a,b)=(-,+),排除 E ,选择 C 难度评级:★★★★

190 . 18493-!-item-!-187;#058&011993 The numbers of books read by 7 students last year were 10, 5, p, q, r, 29, and 20. What was the range of the numbers of books read by the 7 students last year? (1) 5 < p < q (2) p < r < 15

答案:E 题目翻译:7 个学生去年的阅读的书,本数为 10, 5, p, q, r, 29, 20 。这组数的范围是多 少? 仅条件一:r 未知,无法判断,排除 A,D 仅条件二:q 的范围未知,无法判断,排除 B 一二同看:5<p<r<15 q 可以是介于 p 和无限大的任何数,无法判断,排除 C,选择 E 难度评级:★★★★

191 . 18547-!-item-!-187;#058&011999 Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k ? (1) j is divisible by 30. (2) k = 1,000

答案:C 题目翻译:正整数 J 比正整数 K 有更多的质因子吗? 仅条件一: j=30n=1x2x3x5xn 不知道 k,无法判断,排除 A,D 仅条件二:k=1x2x5xm 不知道 j,无法判断,排除 B 一二同看: j is divisible by at least 4 prime numbers, k is divisible by 3 prime numbers. 排除 E,选择 C 难度评级:★★★

192 . 18601-!-item-!-187;#058&012081 Is xy > 0 ?

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(1) x - y > -2 (2) x - 2y < -6

答案:C 仅条件一: x,y can be both positive or negative,排除 A,D 仅条件二:x,y can be both positive or negative,排除 B 一二同看:=> y - 2 < x < 2y - 6 ,y - 2 < 2y - 6, y > 4 => x > 2 ,=> xy > 0 , => (C) 排除 E ,选择 C 难度评级:★★

193 . 18701-!-item-!-187;#058&012184 If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20

答案:D 仅条件一:8-y>10, y<-2, 8-y>8+y ,保留 A,D 仅条件二:x+20>10, x>-10, x+10>x-20 ,排除 A ,选择 D 难度评级:★

194 . 18755-!-item-!-187;#058&012205 If r is the remainder when the positive integer n is divided by 7, what is the value of r ? (1) When n is divided by 21, the remainder is an odd number. (2) When n is divided by 28, the remainder is 3.

答案:B 题目翻译:r 是正整数 n 除以 7 的余数,r 值为多少? 仅条件一:n=7m+r ,n=21k+i=3*7m+i, i={19,17,15,13,11,9,8,7,5,3,1} ,排除 A,D 仅条件二:n=28m+j=4*7m+j, j={3} ,选择 B 难度评级:★★★★

195 . 18858-!-item-!-187;#058&012264 If w, x, y, and z are integers such that (1) wx + yz is odd. (2) wz + xy is odd.
w x

and

y z

are integers, is

w x

+

y z

odd?

答案:B
w 题目翻译:w,x,y,z 都是整数, w x 和 z 也是整数, x + z 是奇数吗?
y y

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仅条件一: suppose wx is odd, either w or x or both could be odd. If w and x are both odd,
w w is odd. If w is even and x is odd, is even. 排除 A,D x x

仅条件二:

w y wz ? xy , 依题意得到的是整数。奇数被整除时也是奇数。选择 B ? ? x z xz

难度评级:★★★★

196 . 18962-!-item-!-187;#058&012363 A recent lunch meeting at a certain club was attended by members and guests. Each member paid $4 for the lunch, and each guest paid $8 for the lunch. How many of the people attending the meeting were members? (1) A total of 20 people attended the meeting. (2) A total of $92 was paid for the lunch.

答案:C 题目翻译:会员付 4 刀,客人付 8 刀,多少会员参加了会议? 仅条件一:设 member 人数=m; guests 人数=g ,问 m=?,m+g=20,只有一个式子, 不充分,排 除 A,D 仅条件二:4m+8g=92, 只有一个式子,不充分,排除 B 一二同看:两个式子已经可以得知 m 为多少,充分,排除 E ,选择 C 难度评级:★★

197 . 19016-!-item-!-187;#058&012397 The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r > 1 ? (1) The greatest common factor of m and p is 2. (2) The least common multiple of m and p is 30.

答案:A 题目翻译:整数 m 和 p,满足,2 < m < p 且 m 不是 p 的因子,p 除以 m 的余数 r,大于 1 吗? 仅条件一: m=2x and p=2y p>m, therefore y>x 2y/2x remainder is at least 2,保留 A,D 仅条件二:30=2x3x5 p=6, m=5, p/m 余 1 p=15, m=6, p/m 余 3, 排除 D ,选择 A 难度评级:★★★

198 . 19116-!-item-!-187;#058&012496 If @ denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the

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value of 1 @ 2 ? (1) n @ 0 = n for all integers n. (2) n @ n = 0 for all integers n.

答案:B 题目翻译:如果@ 被定义为加减乘除中任意一种算法,那么 1 @ 2 的值为多少? 仅条件一:@可以是乘或减,排除 A,D 仅条件二:@只可以是减,选择 B 难度评级:★★

199 . 19170-!-item-!-187;#058&012498 Warehouse W's revenue from the sale of sofas was what percent greater this year than it was last year? (1) Warehouse W sold 10 percent more sofas this year than it did last year. (2) Warehouse W's selling price per sofa was $30 greater this year than it was last year.

题目翻译:今年W货仓从卖沙发得到的收入比去年的大百分之多少? 仅条件一:不知道今年和去年沙发的单价,无解,排除A,D 仅条件二:不知道今年和去年沙发卖的个数,无解,排除B,D 一二同看:有不止一个未知数,参考 prep1 中 ds201,无解,排除 C 难度评级:★★

200 . 19224-!-item-!-187;#058&012506 If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d ? (1) 10^d is a factor of f. (2) d > 6

题目翻译:d 是一个正整数,f 是前 30 个正整数的积,d=? 仅条件一:d 可以为 1,2,3 等,无解,排除 A,D 仅条件二:不知 d 的具体值,无解,排除 B,D 一二同看:{5,10,15,20,25,30,2,4,6,8,?} 可以找出 7 个 5 和 2 的 product。 又 d>6,则 d 一定为 7,有解,排除 E 难度评级:★★★

201 . 19278-!-item-!-187;#058&012507 If k is a line in the xy-plane, what is the slope of k ? (1) The x-intercept of k is 2. (2) The y-intercept of k is 3.

题目翻译:k 的斜率? 仅条件一:只知道 k 在 x 轴的截距,无解,排除 A,D 仅条件二:只知道 k 在 y 轴的截距,无解,排除 B,D
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一二同看:得到分别截距(2,0),(0,3),有解,排除 E 难度评级:★

202 . 19378-!-item-!-187;#058&012570 The numbers x and y are not integers. The value of x is closest to which integer? (1) 4 is the integer that is closest to x + y. (2) 1 is the integer that is closest to x - y.

题目翻译:x, y 不是整数,x 最接近于哪个整数? 仅条件一:x, y 有多种组合,无解,排除 A,D 仅条件二:x, y 有多种组合,无解,排除B,D 一二同看:两式相加得2x靠近5,即2/5,但不知靠近2还是3,无解。排除C 难度评级:★★

203 . 19527-!-item-!-187;#058&012646 What is the result when x is rounded to the nearest hundredth? (1) When x is rounded to the nearest thousandth the result is 0.455. (2) The thousandths digit of x is 5.

题目翻译:x 近似到百分位是多少? 仅条件一:但原数为 0.4546~0.4549 时,近到百分位为 0.45;但当原数是 0.4550~0.4554 时, 近到百分位为 0.46,无解,排除 A,D 仅条件二:不知道百分位为多少,无解,排除 B,D, 一二同看:确定 x 在 0.4550~0.4554 范围内,可确定为 0.46,有解,排除 E 难度评级:★★★

204 . 19581-!-item-!-187;#058&012650 If Mary always takes the same route to work, how long did it take Mary to get to work on Friday? (1) It took Mary 20 minutes to get to work on Thursday. (2) Mary's average speed on her trip to work was 25 percent greater on Thursday than it was on Friday.

题目翻译:Mary 总是走同样的路线上班,周五 Mary 要花多少时间去工作? 仅条件一:仅知道周四花 20 分钟,无解,排除 A,D 仅条件二:不知道周四的所花时间,无解,排除 B,D 一二同看:设周五速度为 a,20/1.25a = 所求时间/a,可得所求时间,有解,排除 E 难度评级:★★★

205 . 19960-!-item-!-187;#058&012914 What was a certain company's revenue last year? (1) Last year the company's gross profit was $4,100.

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(2) Last year the company's revenue was 50 percent greater than its expenses.

题目翻译:去年某个公司的收入? 仅条件一:仅知道利润,无解,排除 A,D 仅条件二:不知道它的花费,无解,排除 B,D 一二同看:利润(4,100)= 1.5Expenses – Expenses= 0.5E 可得 E,进而得出 1.5E,有解,排 除E 难度评级:★★★

206 . 20297-!-item-!-187;#058&013111 In 1984 a certain union had a total of 15,600 members. Was the percent increase in the total number of members in the union from 1984 to 1985 greater than that from 1985 to 1986 ? (1) From 1984 to 1985 the total number of members in the union increased by 781, and from 1985 to 1986 the total number of members in the union again increased by 781. (2) In 1985 the union had a total of 16,381 members, and in 1986 the union had a total of 17,162 members .

题目翻译:1984 一个团体有 15,600 会员,1984-1985 会员增加的百分比比 1985-1986 增加的 大吗? 仅条件一:可知分别三年会员的人数,可得增长比例,有解,排除 B,C,E 仅条件二:可知分别三年会员的人数,可得增长比例,有解,排除 A,C,E 难度评级:★

207 . 20351-!-item-!-187;#058&013123

At a certain theater, the cost of each adult's ticket is $5 and the cost of each child's ticket is $2. What was the average (arithmetic mean) cost of all the adults' and children's tickets sold at the theater yesterday? (1) Yesterday the ratio of the number of children's tickets sold at the theater to the number of adults' tickets sold at the theater was 3 to 2. (2) Yesterday 80 adults' tickets were sold at the theater. 题目翻译: 每个大人的票价和每个小孩的票价分别是 5 刀和 2 刀, 昨天所有大人和小孩的平 均票价是多少? 仅条件一: (3X 乘以 2 + 2X 乘以 5)/5X 可得,有解,排除 B,C,E 仅条件二:不知道小孩票多少张,无解,排除 B,D 难度评级:★★

208 . 20405-!-item-!-187;#058&013127 At a certain store, each notepad costs x dollars and each marker costs y dollars. If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4 markers instead? (1) Each notepad costs less than $1. (2) $10 is enough to buy 11 notepads.

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题目翻译:每个笔记本和每个书签分别花 X 刀和 y 刀,10 刀购买 5 个笔记本和 3 个书签, 10 刀够买四个笔记本和 4 个书签吗? 仅条件一:仅知道 X<1,无解,排除 A,D 仅条件二:不知道书签的价格,无解,排除 B,D 一二同看:不知 y 的价格或者 x 和 y 的关系,无解,排除 C 难度评级:★★

209 . 20459-!-item-!-187;#058&013172 The cost of each adult's ticket for a certain concert was $30, and the cost of each child's ticket for the concert was $24. If Hannah purchased tickets for this concert, what was the average (arithmetic mean) cost per ticket? (1) Hannah purchased twice as many children's tickets as adults' tickets. (2) Hannah purchased 4 children's tickets.

题目翻译: 每个大人和每个小孩的票价分别是 30 刀和 24 刀。 H 买的票的平均花费是多少? 仅条件一:参考 prep2 ds 207,有解,排除 B,C,E 仅条件二:不知购买了多少张成人票,排除 B,D 难度评级:★★

210 . 20513-!-item-!-187;#058&013256 For each order, a mail-order bookseller charges a fixed processing fee and an additional shipping fee for each book in the order. Rajeev placed five different orders with this bookseller--an order for 1 book in January, an order for 2 books in February, an order for 3 books in March, an order for 4 books in April, and an order for 5 books in May. What was the total of Rajeev's processing and shipping fees for these five orders? (1) Rajeev's processing and shipping fees were $1.00 more for his order in March than for his order in January. (2) The total of Rajeev's shipping fees for the five orders was $7.50.

题目翻译:每个订单,订单书商收取固定费用加每一本书收的费用。R 订了 5 个订单,1 月 订了 1 本书, 2 月 2 本书, 3 月 3 本书, 4 月 4 本书, 5 月 5 本书, 所花的总费用? 仅条件一: 但仍不知 X,无解,排除 A,D 仅条件二: 但仍不知 X,无解,排除 B,D 一二同看:仍不知 X,无解,排除 C 难度评级:★★★

211 . 20614-!-item-!-187;#058&013294 A certain economics class consists of 50 women and 30 men. How many of the men in the class are business majors? (1) 40 percent of the women in the class are business majors. (2) 50 percent of all the people in the class are business majors.

题目翻译:经济学课包括 50 女 30 男,男中有多少事商业专业?
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仅条件一:不知男的状况,无解,排除 A,D 仅条件二:不具体知道男的状况,无解,排除 B,D 一二同看:50 乘以 0.4,有 20 个女生是商业专业,一共有 0.5 乘以 80,即 40 个人商业专业, 可得 20 个男生是商业专业,有解,排除 E 难度评级:★★★

212 . 20668-!-item-!-187;#058&013295 For a certain play performance, adults' tickets were sold for $12 each and children's tickets were sold for $8 each. How many children's tickets were sold for the performance? (1) The total revenue from the sale of adults’ and children’s tickets for the performance was $5,040. (2) The number of adults’ tickets sold for the performance was tickets sold for the performance.
1 3

the total number of adults’ and children’s

题目翻译:成人和小孩的票价分别是 12 刀和 8 刀,卖了多少小孩的票? 仅条件一:不知成人票卖了多少,成人票和小孩票数量关系,无解,排除 A,D 仅条件二:不知任意一个具体卖了多少张,无解,排除 B,D 一二同看:可得分别卖了多少张票,有解,排除 E 难度评级:★★ Caution!:若是求比例,则条件二可以

213 . 20722-!-item-!-187;#058&013303 Linda, Robert, and Pat packed a certain number of boxes with books. What is the ratio of the number of boxes of books that Robert packed to the number of boxes of books that Pat packed? (1) Linda packed 30 percent of the total number of boxes of books. (2) Robert packed 10 more boxes of books than Pat did.

题目翻译:R 打包的箱子数量与 P 打包的数量比? 仅条件一:不知 R 或 P 的情况,无解,排除 A,D 仅条件二:不知比例关系,无解,排除 B,D 一二同看:不知 R 和 P 的关系或它们任意一个的数量,无解,排除 C 难度评级:★★

214 . 20776-!-item-!-187;#058&013419 Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees? (1) Two of the interior angles of ABCD are right angles. (2) The degree measure of angle ABC is twice the degree measure of angle BCD.

题目翻译:四边形的一个内角等于 60 度吗? 仅条件一:有两个是直角,无解,排除 A,D 仅条件二:角 ABC 是 BCD 的两倍,无解,排除 B,D
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一二同看:不知 ABC 是否是直角。两种情况 90,90,45,135;90,90,60,120。无解,排除 C 难度评级:★★★

215 . 20830-!-item-!-187;#058&013425 On the number line, the distance between point A and point C is 5 and the distance between point B and point C is 20. Does point C lie between point A and point B ? (1) The distance between point A and point B is 25. (2) Point A lies to the left of point B.

题目翻译:数轴上,AC 的距离是 5,BC的距离是20,C在点A和B之间吗? 仅条件一: AB=25 时两种情況, 一为 B--------------------C----A, 另一为 A----C--------------------B, C 都在 AB 之间,有解,排除B,C,E 仅条件二: A 在 B 左边, 两种情況。 一为 A----C--------------------B, 另一为 C----A---------------B, C 的位置不一样,无解,排除B,D 难度评级:★★★

216 . 20930-!-item-!-187;#058&013466 Is the three-digit number n less than 550 ? (1) The product of the digits in n is 30. (2) The sum of the digits in n is 10.

题目翻译:三位数n小于550吗? 仅条件一:30=2x3x5 或 6x5 所 n 有可能为 235,253,325,352,523,532 或 650,560, 在前面的情況,n 既可能大于也可能小于550,无解,排除A,D 仅条件二:三位相加为 10 可能性多种:如 910 或 109,无解,排除B,D 一二同看:从(1)n 的可能性, (2)缩小范围,n 为 235,253,325,352,523,532 时,其 和都等于 10,且值都小于 550,有解,排除E 难度评级:★★★★

217 . 20984-!-item-!-187;#058&013473 If n is a three-digit positive integer, what is the sum of the digits of n ? (1) The hundreds digit of n is 3 times the units digit. (2) The hundreds digit of n is 3 more than the tens digit.

题目翻译:n是一个三位正整数,n的各数位和是多少? 仅条件一:不知十位数,无解,排除A,D 仅条件二:不知个位数,无解,排除B,D 一二同看:不知任意一个数的大小,无解,排除C 难度评级:★★

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218 . 21130-!-item-!-187;#058&013592 The retail price of a certain refrigerator is 1.6 times its wholesale price. What is the difference between the retail price and the wholesale price of the refrigerator? (1) The wholesale price of the refrigerator is $200. (2) The retail price of the refrigerator is $320.

题目翻译:一种冰箱的零售价是它的批发价的1.6倍,零售价和批发价之间的价格差? 仅条件一:可知零售价和批发价各多少,有解,排除B,C,E 仅条件二:可知零售价和批发价各多少,有解,排除A,C,E 难度评级:★

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