﻿ GRE数学考前热身试题-百利天下GRE # GRE数学考前热身试题

GRE数学考前热身试题,GRE数学

1.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 ?

2. 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

3.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

4.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

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

5. 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

6.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 determine which of the integers in the answer choices is a divisor of every　positive integer n in S, you must first understand the integers that are in S. Note　that in this question you are given information about n2, not about n itself.　Therefore, you must use the information about n2 to derive information about n.　The fact that n2 is a multiple of both 24 and 108 implies that n2 is a multiple　of the least common multiple of 24 and 108. To determine the least common　multiple of 24 and 108, factor 24 and 108 into prime factors as (23)(3) and　(22)(33), respectively. Because these are prime factorizations, you can conclude　that the least common multiple of 24 and 108 is (23)(33).　Knowing that n2 must be a multiple of (23)(33) does not mean that every　multiple of (23)(33) is a possible value of n2, because n2 must be the square of an　integer. The prime factorization of a square number must contain only even　exponents. Thus, the least multiple of (23)(33) that is a square is (24)(34). This is　the least possible value of n2, and so the least possible value of n is (22)(32), or　36. Furthermore, since every value of n2 is a multiple of (24)(34), the values of n are the positive multiples of 36; that is, S　{36, 72, 108, 144, 180, . . .} .　The question asks for integers that are divisors of every integer n in S, that　is, divisors of every positive multiple of 36. Since Choice A, 12, is a divisor of 36,　it is also a divisor of every multiple of 36. The same is true for Choice C, 36.　Choices B and D, 24 and 72, are not divisors of 36, so they are not divisors of　every integer in S. The correct answer consists of Choices A and C.

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。

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