GRE_OG_数学精选

1.y=2x2+7x – 3

x y

本体答案不确定。我开始做的时候被题目放了烟雾弹，以为要经过什么特别处理，像配方啥的。但配着配着就感觉不对劲，x与y只有函数关系，没有绝对的大小关系嘛。。。汗

2.

The figure above shows the graph of a function f, defined by f(x)=|2x|+4 for all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f ? A g(x)=x–2 B g(x)=x+3 C g(x)=2x – 2 D g(x)=2x+3 E g(x)=3x – 2

这个题就是问两个函数图象相交的问题，根据观察，要与这个折线相交的直线的斜率满足的条件是要么是正斜率比2大，要么是负斜率比-2小，因此只能选E了。

3.Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and is $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees in the company? Indicate all such amounts. A $26,000 B $28,000 C $29,000

I

新GRE《OG》数学题精选和解答，ＣＤ竹林中人编 II

D $30,000 E $31,000 F $32,000 G $34,000

本题我们要注意到题目中的more than twice的字眼，我们当做twice算的时候，结果是（25000*2+35000）/3约等于28333，因为有more than，所以选的答案要么是比前面这个数大，要么小，又由于more的是X部门的，那么肯定会将平均工资给拉低了，因此，选比前面那个数小的答案，AB都可以了。。

4.Working alone at its constant rate, machine A produces k car parts in 10 minutes. Working alone at its constant rate, machine B produces k car parts in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k car parts? ____________minutes

这类题目小学时候经常遇到，相信很多人都是这种感受哈 1/（1/10+1/15）=6min

1)If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008 ? A $727,200 B $792,000 C $800,000 D $880,000 E $968,000

直接算，800000*（1+10%）*（1-10%）=792000，即B

2)At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008 ?

Give your answer to the nearest 0.1 percent. ___________%

直接算，1/（1-8%）=108.7%（约等于） 3)Which of the following statements must be true? Indicate all such statements.

A For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores.

B The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006.

II

新GRE《OG》数学题精选和解答，ＣＤ竹林中人编III

C The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006.

本题A选项一看到就可以排除了，涉及到两个店的绝对量的比较，这个不确定，没有告诉绝对值。B选项是把两个增长的比例简单地算术相加。肯定错了。所以C肯定是对的了。。算一下也是的确是对的。。 6.A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy? A 9 B 10 C 11 D 12 E 20

这个题首先就可以想到单价越便宜的我就能买的越多，因为它没有说两种笔一定要都买。

7.A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a number in the list that is 2 standard deviations above the mean, what is the value of x ?

x=_8+2.5*2=13_这道题不知怎么的，读题的时候度饶了，感觉很费解，什么是两个标准差，以为是个什么特殊的东西，后来问了同学才知道这就是个简单的计算题，没啥特别的，我的个汗啊，考试的时候我碰到了，我肯定错了。。

8.Frequency Distribution for List X Number 1 2 3 5 Frequency 10 20 18 12 Frequency Distribution for List Y Number 6 7 8 9 Frequency 24 17 10 9

List X and list Y each contain 60 numbers. Frequency distributions for each list are given above. The average (arithmetic mean) of the numbers in list X is 2.7, and the average of the numbers in list Y is 7.1. List Z contains 120 numbers: the 60 numbers in list X and the 60 numbers in list Y.

Quantity A Quantity B

The average of the 120numbers in list Z The median of the 120 numbers in list Z A中，平均数肯定就是两组的平均数的和的一半，也就是（2.7+7.1）/2=4.9，因为两组的人数相同，而B中median就是（5+6）/2=5.5，所以就是B了。。 9.The figure above shows the graph of the function f in the xy-plane. What is the value of f ( f (–1)) ?

III

新GRE《OG》数学题精选和解答，ＣＤ竹林中人编IV

A –2 B –1 C 0 D 1 E 2

这个题就是读图题了，一重重的往外算就好了，f (–1)=2，f（2）=1，即D 10.By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution? A 10% B 13% C 15% D 19% E 26%

这个题小学也经常遇到，（3*8%+7+18%）/（7+3）=15%

11.Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer? A 0.5 B 0.6 C 0.7 D 0.8 E 0.9

这个就是组合的计算了，C580/C700=0.68（约等于），所以选C吧，这个题可以用下那个计算器了。

12.Line k lies in the xy-plane. The x-intercept of line k is –4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k ?

Give your answer as a fraction.__3/4_____

IV

22V 新GRE《OG》数学题精选和解答，ＣＤ竹林中人编

这个题先求出那条线段的中点（2,9/2），然后斜率就是（9/2）/（2-（-4））=3/4

13.

In the course of an experiment, 95 measurements were recorded, and all of the measurements were integers. The 95 measurements were then grouped into 7 measurement intervals. The graph above shows the frequency distribution of the 95 measurements by measurement interval.

Quantity A Quantity B

The average (arithmetic The median of the 95 mean) of the 95 measurements Measurements

这个题我觉得可以估计，median应该在6-10这段，而average呢，根据图表判断，左边的两段和右边的五段占总人数应该是差不多对半分，那么平均数就应该是向高处拉了，这个是经验估计。当然也可以通过算，我觉得这个题去算的话，量相对大些。。。答案为A

14.The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively. Quantity A Quantity B The value at the 75th 750 percentile of the distribution of X

这个题，我做的时候是根据图像做的，在正态分布的函数图象上，60%——90%之间的这段是个下凸的，所以当取750这个自变量的时候，对应的函数值应该是比650和850对应函数值的平均值小的，大家画个图就可以很直观的看出来了。所以750对应的白分比应该是比75%小，选项是Ｂ 15.If 1+x+x2+x3=60, then the average (arithmetic mean) of x, x2, x3, and x4 is equal to which of the following? A 12x B 15x C 20x

V

新GRE《OG》数学题精选和解答，ＣＤ竹林中人编VI

D 30x E 60x

这个题直接在等式的两边乘以ｘ就好了，然后除以４，答案就是Ｂ

16.

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R ? A (3, 2) B (3, 3) C (4, 4) D (5, 2) E (6, 2)

这个题直接读图，应该有Ｑ的坐标减去Ｐ的坐标等于Ｒ的坐标减去Ｏ的坐标，其实也就是两个向量是相等的，Ｏ又恰好是原点，那么Ｒ的坐标就是ＱＰ的向量坐标了，即（６,２）Ｅ选项

17.Let S be the set of all positive integers n such that n2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?

Indicate all such integers. A 12 B 24 C 36 D 72

这个题有点小复杂，我先把ＯＧ上的解答贴上来。再写我自己的

To\r  determine\r  which\r  of\r  the\r  integers\r  in\r  the\r  answer\r  choices\r  is\r  a\r  divisor\r  of\r  every\r  positive\r  integer\r  n\r  in\r  S,\r  you\r  must\r  first\r  understand\r  the\r  integers\r  that\r  are\r  in\r  S.\r  Note\r  that\r  in\r  this\r  question\r  you\r  are\r  given\r  information\r  about\r  n2,\r  not\r  about\r  n\r  itself.\r  Therefore,\r  you\r  must\r  use\r  the\r  information\r  about\r  n2\r  to\r  derive\r  information\r  about\r  n.\r  The\r  fact\r  that\r  n2\r  is\r  a\r  multiple\r  of\r  both\r  24\r  and\r  108\r  implies\r  that\r  n2\r  is\r  a\r  multiple\r  

VI

VII 新GRE《OG》数学题精选和解答，ＣＤ竹林中人编

of\r  the\r  least\r  common\r  multiple\r  of\r  24\r  and\r  108.\r  To\r  determine\r  the\r  least\r  common\r  multiple\r  of\r  24\r  and\r  108,\r  factor\r  24\r  and\r  108\r  into\r  prime\r  factors\r  as\r  (23)(3)\r  and\r  (22)(33),\r  respectively.\r  Because\r  these\r  are\r  prime\r  factorizations,\r  you\r  can\r  conclude\r  that\r  the\r  least\r  common\r  multiple\r  of\r  24\r  and\r  108\r  is\r  (23)(33).\r  

Knowing\r  that\r  n2\r  must\r  be\r  a\r  multiple\r  of\r  (23)(33)\r  does\r  not\r  mean\r  that\r  every\r  multiple\r  of\r  (23)(33)\r  is\r  a\r  possible\r  value\r  of\r  n2,\r  because\r  n2\r  must\r  be\r  the\r  square\r  of\r  an\r  integer.\r  The\r  prime\r  factorization\r  of\r  a\r  square\r  number\r  must\r  contain\r  only\r  even\r  exponents.\r  Thus,\r  the\r  least\r  multiple\r  of\r  (23)(33)\r  that\r  is\r  a\r  square\r  is\r  (24)(34).\r  This\r  is\r  the\r  least\r  possible\r  value\r  of\r  n2,\r  and\r  so\r  the\r  least\r  possible\r  value\r  of\r  n\r  is\r  (22)(32),\r  or\r  36.\r  Furthermore,\r  since\r  every\r  value\r  of\r  n2\r  is\r  a\r  multiple\r  of\r  (24)(34),\r  the\r  values\r  of\r  n\r  are\r  the\r  positive\r  multiples\r  of\r  36;\r  that\r  is,\r  S{36,\r  72,\r  108,\r  144,\r  180,\r  .\r  .\r  .}\r  .\r  

The\r  question\r  asks\r  for\r  integers\r  that\r  are\r  divisors\r  of\r  every\r  integer\r  n\r  in\r  S,\r  that\r  is,\r  divisors\r  of\r  every\r  positive\r  multiple\r  of\r  36.\r  Since\r  Choice\r  A,\r  12,\r  is\r  a\r  divisor\r  of\r  36,\r  it\r  is\r  also\r  a\r  divisor\r  of\r  every\r  multiple\r  of\r  36.\r  The\r  same\r  is\r  true\r  for\r  Choice\r  C,\r  36.\r  Choices\r  B\r  and\r  D,\r  24\r  and\r  72,\r  are\r  not\r  divisors\r  of\r  36,\r  so\r  they\r  are\r  not\r  divisors\r  of\r  every\r  integer\r  in\r  S.\r  The\r  correct\r  answer\r  consists\r  of\r  Choices\r  A\r  and\r  C.\r  

这个意思就是先求出２４和１０８的最小公倍数，然后通过加倍使其成为一个整数的平方，这样就可以找出一系列的ｎ了，这些ｎ的公公因数应该有哪些？我找了前面的两个，３６和７２，所以ＡＣ可以选出来了，之后的所有数肯定包含了这两个选项，而ＢＤ因为不满足前面这两数，所以就排除了。\r  

18.The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4inches.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class? Indicate all such statements.

A The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.

B The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.

C The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.

分析：在数轴上我们可以画出一段表示女生身高范围，另一段表示男生身高范围，

Ａ选项告诉我们的是男生最高的比女的最高的高５．８ｉｎｃｈ，那么我们就可以确定两段的相对位置了，因此总的身高范围就可以确定了。选项A就是对的了。

B选项，由于没有告诉我们男女生的人数，所以这个是无法确定的

C选项，这个选项跟上面的B差不多，没法确定。附上OG的解答，以作参考：

Choice\r  B\r  provides\r  information\r  about\r  one\r  of\r  the\r  centers\r  of\r  the\r  data—the\r  median;\r  it\r  does\r  not\r  say\r  anything\r  about\r  how\r  spread\r  out\r  the\r  data\r  are\r  around\r  that\r  center.\r  You\r  are\r  given\r  that\r  the\r  median\r  height\r  of\r  the\r  males\r  is\r  1.1\r  inches\r  greater\r  than\r  that\r  of\r  the\r  females.\r  First\r  note\r  that\r  it\r  is\r  possible\r  for\r  two\r  different\r  sets\r  of\r  data\r  to\r  have\r  the\r  same\r  median\r  but\r  have\r  very\r  different\r  ranges.\r  Choice\r  B\r  gives\r  the\r  

VII

VIII 新GRE《OG》数学题精选和解答，ＣＤ竹林中人编

difference\r  between\r  the\r  medians\r  of\r  the\r  male\r  heights\r  and\r  the\r  female\r  heights,\r  without\r  giving\r  the\r  actual\r  medians.\r  However,\r  even\r  if\r  you\r  knew\r  the\r  medians,\r  the\r  fact\r  that\r  the\r  ranges\r  can\r  vary\r  widely\r  indicates\r  that\r  the\r  range\r  of\r  the\r  heights\r  of\r  the\r  entire\r  class\r  can\r  also\r  vary\r  widely.\r  

It\r  is\r  possible\r  to\r  construct\r  examples\r  of\r  heights\r  of\r  students\r  that\r  satisfy\r  all\r  of\r  the\r  information\r  in\r  the\r  question\r  and\r  in\r  Choice\r  B\r  but\r  have\r  different\r  ranges\r  for\r  the\r  heights\r  of\r  the\r  entire\r  class.\r  Here\r  are\r  two\r  such\r  examples,\r  each\r  of\r  which\r  has\r  only\r  three\r  females\r  and\r  three\r  males.\r  Although\r  the\r  examples\r  are\r  small,\r  they\r  illustrate\r  the\r  fact\r  that\r  the\r  range\r  of\r  the\r  heights\r  of\r  the\r  entire\r  class\r  can\r  vary.\r  In\r  both\r  examples,\r  the\r  range\r  of\r  female\r  heights\r  is\r  13.2,\r  the\r  range\r  of\r  male\r  heights\r  is\r  15.4,\r  and\r  the\r  difference\r  between\r  the\r  median\r  heights\r  is\r  1.1\r  inches.\r  Example\r  1\r  

Female\r  heights:\r  50.0\r  56.6\r  63.2\r  which\r  have\r  a\r  median\r  of\r  56.6\r  Male\r  heights:\r  50.0\r  57.7\r  65.4\r  which\r  have\r  a\r  median\r  of\r  57.7\r  Range\r  of\r  heights\r  of\r  entire\r  class:\r  15.4\r  Example\r  2\r  

Female\r  heights:\r  50.0\r  56.6\r  63.2\r  which\r  have\r  a\r  median\r  of\r  56.6\r  Male\r  heights:\r  51.0\r  57.7\r  66.4\r  which\r  have\r  a\r  median\r  of\r  57.7\r  Range\r  of\r  heights\r  of\r  entire\r  class:\r  16.4\r  

Therefore,\r  Choice\r  B\r  does\r  not\r  provide\r  sufficient\r  additional\r  information\r  to\r  determine\r  the\r  range\r  of\r  the\r  heights\r  of\r  the\r  entire\r  class.\r  

Choice\r  C\r  provides\r  information\r  about\r  another\r  center\r  of\r  the\r  data—the\r  

average.\r  You\r  are\r  given\r  that\r  the\r  average\r  height\r  of\r  the\r  males\r  is\r  4.6\r  inches\r  greater\r  than\r  that\r  of\r  the\r  females.\r  However,\r  like\r  Choice\r  B,\r  the\r  statement\r  gives\r  no\r  information\r  about\r  how\r  spread\r  out\r  the\r  data\r  are\r  around\r  that\r  center.\r  Again,\r  it\r  is\r  possible\r  for\r  two\r  different\r  sets\r  of\r  data\r  to\r  have\r  the\r  same\r  average\r  but\r  have\r  very\r  different\r  ranges.\r  Examples\r  similar\r  to\r  the\r  two\r  examples\r  above\r  can\r  be\r  constructed\r  that\r  satisfy\r  all\r  of\r  the\r  information\r  in\r  the\r  question\r  and\r  in\r  Choice\r  C\r  but\r  have\r  different\r  ranges\r  for\r  the\r  heights\r  of\r  the\r  entire\r  class.\r  Therefore,\r  Choice\r  C\r  does\r  not\r  provide\r  sufficient\r  additional\r  information\r  to\r  determine\r  the\r  range\r  of\r  the\r  heights\r  of\r  the\r  entire\r  class.\r  

19.A random variable Y is normally distributed with a mean of 200 and a standard

deviation of 10.

Quantity A Quantity B The probability of the event 1/6 that the value of Y is greater than 220

这个可以复习下那个正态分布的图了，OG294面。220对应的就是mean+两个标准差了，那么220以下的比例是（50+34+14）%了，在220以上的就是1减去前面这个数，比1/6要小。B

20.In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?_____121_____students

这个题我开始以为是那种集合性质的，用121+142-236，算的，但对答案发

VIII

新GRE《OG》数学题精选和解答，ＣＤ竹林中人编IX

现错了，细看题目才知道，这两种考试并不是全集，所以最多两种同时考的就是报的少的那个了。。。

21.The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true? Indicate all such statements.

A The price of the book was less than $9.50. B The price of the book was greater than $6.90. C The sales tax was less than $0.45.

如果设书的价格是x，那么总的支出是1.04x，根据题意有（10-3）<1.04x<10,解得6.7322.Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above? Indicate all such statements. A DBC is an equilateral triangle. B ABD is an isosceles triangle.

C The length of BC is equal to the length of AD. D The length of BC is 10. E The length of AD is 10

只告诉了三角形是直角三角形和一条直角边，要求我们补充条件可以求得三角形的面积。只能用排除法。Ａ说三角形ＤＢＣ是等边的，角Ｃ就是６０度了，其他的便也就可以求出来了，面积就可以求。Ｂ说ＡＢＤ是等腰三角形，这个没意义，因为没说那两个边是等的，比如如果ＡＢ＝ＡＤ，是没法求的，Ｃ说ＢＣ＝AD，这个条件是没有意义的，因为我们的D点可以移动，当三角形的大小发生变化时，我们总可以找到对应的D点使得AD=BC，D选项说BC=10，这就可以求了，E说AD的长是10，这个同样没意义。所以选AD。

23.The fabric needed to make 3 curtains sells for $8.00 per yard and can be purchased only by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains? A $40.00 B $38.40

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X 新GRE《OG》数学题精选和解答，ＣＤ竹林中人编

C $24.00

D $16.00 E $12.80

Since\r  1.6\r  yards\r  of\r  fabric\r  are\r  required\r  for\r  each\r  curtain,\r  it\r  follows\r  that\r  (3)(1.6),\r  or\r  4.8,\r  yards\r  of\r  fabric\r  are\r  required\r  to\r  make\r  the\r  3\r  curtains.\r  The\r  fabric\r  can\r  be\r  purchased\r  only\r  by\r  the\r  full\r  yard,\r  so\r  5\r  yards\r  of\r  fabric\r  would\r  need\r  to\r  be\r  purchased.\r  Since\r  the\r  fabric\r  sells\r  for\r  $8.00\r  per\r  yard,\r  the\r  total\r  cost\r  of\r  the\r  fabric\r  is\r  $40.00.\r  The\r  correct\r  answer\r  is\r  Choice\r  A.\r  

还是用汉语解释下吧，一共三个窗帘，每个1.6m，那么一共要4.8m，由于不能零卖，只能整数的卖，所以买5m，一共是5*8=40了。\r  

25.In the xy-plane, the point with coordinates (–6, –7) is the center of circle C. The point with coordinates (–6, 5) lies inside C, and the point with coordinates (8, –7) lies outside C. If m is the radius of C and m is an integer, what is the value of m ? m =_____

这个题大家可以画个坐标图，标出那几个点，（-6,5）在圆内，那么半径m >5-(-7)=12（之所以能这么算，是因为圆心坐标跟这个点的横坐标相同）,而点（8，-7）在圆外，那么m<8-(-6)=14,又因为m是整数，因而m=13了

26.What is the least positive integer that is not a factor of 25! and is not a prime number? A 26 B 28 C 36 D 56 E 58

这个题，你看25！里面包括了2到25的所有factor了，所以你看26=2*13,28=2*14,36=2*18,56=7*8，而只有58=2*29,29不在里面，所以就选这个了

27If 1 is expressed as a terminating decimal, how many nonzero digits 1/[(211)(517)]

will the decimal have? A One B Two C Four D Six E Eleven

将分子转化下，使之成为以10为底数的指数，由此可以判断小数点的位数了，（211)(517 ）=1011*56=（1/）*1017，由此可知，倒过来后，非零数位有两位，6和4.

28.Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below.

(a) What are the range, the three quartiles, and the interquartile range of the

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新GRE《OG》数学题精选和解答，ＣＤ竹林中人编XI

measurements?

(b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?

a.这个范围就是146-105=41了，四分之一分位点在114这儿，四分之二分位点在118这儿，四分之三分位点在126这儿，四分位差为126-114=12,。

b..在80%这儿是130，在75%这儿是126，那么126至130之间是5%了，对应的measurements是800*4%=40；

29.The figure shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters.

(a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall?

(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05

a.65和75之间，刚好是2个的标准差，因此对应的就是34%+14%=48%了，对应的企鹅是3000*48%=1440了。

B.算的结果应该是2%+14%=16%，最经的0.05应嘎是0.15了

以上解答纯属一家之言，如有异议，大可不必相信我的，大家可以讨论交流，谢谢！

——————————By 竹林中人 2011年12月17日晚

XI