GRE数学考前热身试题-智课教育旗下智课教育.pdf

智 课 网 G R E 备 考 资 料 GRE数学考前热身试题 智课教育旗下智课教育 本系列为同学们整理了GRE数学中出现的一些高频高质量的题目 并配有解析 希望同学们认真备考 都能取得好成绩 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 Give your answer as a fraction 3 4 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 20 x D 30 x E 60 x 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 a