课件xdf500题解释版

1、GMAT 数学 XDF500 题（PS 部分）第一版XDF500 团队 编著获得本文档最新内容，关注上面的美研项目本文档学习交流，不得用于任何商业用途：留学资讯1A grocery store purchased crates of 40 oranges each for $5.00 per crate and then sold each orange for $0.20.What was the store's gross profit on each crate of oranges?(A) $3.00(B) $6.00(C) $8.00 (D) $10.00(E) $13 00

2、A收入-成本=利润1总收入用 40 乘以 0.2 再减去进货成本考点难度思路2The product P of two primbers is between 9 and 55.If one of the primbers isgreater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =(A) 15(B) 33(C) 34(D) 46(E) 51E质数 因数1其中一个质数可以为 3 或 5 另一个为 17 19 或 23 计算出来考点难度思路3, then m =If(A)

3、17(B) 18(C) 34(D) 35(E) 36D考点 指数运算难度 2思路 分母的数字分解质因数 找到 2 和 5 的指数对应1：留学资讯4The value ofis closest to which of the following?(A) 1(B) 10(C) 102(D) 103(E) 104B小数分数科学计数法1分母减号后面的数对于前面的数都可以忽略不计考点难度思路5For every positive even integer n, the function h(n) is defined to be the product of all the even integers

4、from 2 to n, inclusive.If p is the smallest prime factor of h(100) + 1, then p is(A) between 2 and 10(B) between 10 and 20(C) between 20 and 30(D) between 30 and 40(E) greater than 40E定义新运算 质数 因数4h(100)可以被 250 任何数整除考点难度思路那么加 1 之后不能被 250 任何数整除2：留学资讯6A flower arrangement consists of 30 roses, each of

5、which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?(A) 5(B) 10(C) 15(D) 20(E) 25D概率 比例2抽到概率 2 比 1 那么数量也为

6、 2 比 1 一共 30考点难度思路7Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?(A) $27,000(B)

7、 $30,000 (C) $33,000 (D) $36,000 (E) $63,000C描述统计学 比例2最高 最低=30000 那么都提高 10% 差值也增加了 10%考点难度思路3：留学资讯8In the figure above, the radius of the circle with center O is 1 and BC = 1.What is the areaof triangular region ABC ?(A) 2/2(B) 3/2(C) 1(D) 2(E) 3B考点难度思路平面几何2半径为 1 直径为 2 直径所对应圆周角为直角 所以 ABC 为直角三角形 算出 A

8、B 边9Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value ininterest.If that interest was approximately 6.5 percent of thebond'ssellingprice,approximately what was the bond's selling price?(A) $4,063(B) $5,325(C) $5,351(D) $6,000(E) $6,154E比例25000 的 8%为 400

9、考点难度思路是销售额的 6.5% 那么 400 除以 0.065 算出4：留学资讯10If m lies between the integers p and s on the number line shown, which of the following is apossible value for m ?(A) 17(B) (C) 2.9 (D) 20/4 (E) 10/3E数形结合2结合数轴看出 P 为 3 S 为 4 找到选项中 3-4 之间的值考点难度思路11At a speed of 50per hour, a certain car uses 1 gallon of gaso

10、line every 30.If theper hour,car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50the amount of gasoline used would be what fraction of a full tank?(A) 3/25(B) 11/36 (C) 7/12(D) 2/3(E) 25/36E比例35 乘以 50 一共行驶了 250 英里考点难度思路加仑250 除以 30 算出消耗了 25/3 加仑的油再比上总量 125：留学资讯12In a certai

11、n board game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?(A)(B)(C)(D)(E)1/81/61/53/234/23E概率2SH

12、 卡的数量 8 张 比上剩余所有卡的数量 46 张考点难度思路13For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence

13、 1,-3, 2, 5, -4, -6 ?(A) One(B) Two(C) Three(D) Four(E) FiveC数列4题干意思为相邻两项乘积为负的情况发生的次数考点难度思路并且注意数列不要再排序 就按照题干给定的找出符合要求的情况一共 3 次6：留学资讯14It takes Carlos 9 minutes to drive from home to work at an average rate of 22per hour.How many minutes will it take Carlos to cycle from home to work along the same r

14、oute at anaverage rate of 6per hour?(A) 26(B) 33(C) 36(D) 44(E) 48B比例2距离 S 相同 所用时间和行驶速度成反比 速度是之前的 6/22考点难度思路那么时间是之前的 22/6乘以 9 得到15If a = 1 and b = -2, then (2a2 + b)(x + y) + (a + b)(x - y) =(A) 0(B) 2x(C) y - x(D) x - y(E) x + yC解方程1代入计算即可考点难度思路7：留学资讯16The formula F = 9C/5 + 32 gives the relationsh

15、ip between the temperature in degrees Fahrenheit, F, and the temperature given in degrees Celsius, C. If the temperature is 85 degrees Fahrenheit, what is the temperature, to the nearest degree, in degrees Celsius?(A) 18(B) 23(C) 29(D) 47(E) 51C比例2纯碎考点难度思路换算之间转化 代入计算即可17In a certain game, the units

16、of currency of three countries are the crown, the shield, and the pound, respectively. If 2 crowns equal 3 shields and 3 shields equal 4 pounds, how many crowns equal 18 pounds?(A) 9(B) 16(C) 18(D) 32(E) 36A比例2C 比 S 比 P=2 比 3 比 4考点难度思路那么 18P=9C8：留学资讯18D因式分解2直接平方差公式展开考点难度思路19There are 10 children in

17、a company's day-care center, and a pair of children is to be selected to play a game.At most, how many different pairs are possible?(A) 100(B) 90(C) 50(D) 45(E) 25D排列组合210 个小孩任选 2 个考点难度思路顺序不同对于结果没有影响 所以用组合 10C29：留学资讯2038, 69, 22, 73, 31, 47, 13, 82Which of the following numbers is greater than t

18、hree-fourths of the numbers but less than one-fourth of the numbers in the list above?(A) 56(B) 68(C) 69(D) 71(E) 73D比大小1一共 8 个数 从小到大顺序排好 找到第 6 和第 7 个 之间的是考点难度思路21If xy = 1, what is the value of 2(x+y)2 /2(x-y)2 ?(A)(B)(C)(D)(E)2481632D指数运算2底数不变考点难度思路指数相减 指数平方展开 2 次项消掉 还剩下 2XY-(-2XY)得出10：留学资讯22The v

19、alue of the expression above is closest to which of the following?(A) 0.0001(B) 0.001(C) 0.1(D) 1(E) 10C小数分数2的 0.0001 对于 1 和分母的 10 都可以忽略不计 而分母的 0 04 对于 10 也可以忽略考点难度思路不计23A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40

20、percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?(A) $40(B) $60(C) $80(D) $90(E) $100E收入 成本 利润3售价=150+0.4*售价考点难度思路算出售价为 250 再减去 150 得出11：留学资讯24The circle shown has center O

21、and radius 4.What is the area of the shaded region?(A)(B)(C)(D)(E)34 6 8 12E平面几何 圆1阴影面积为圆面积的 3/4 圆面积公式R 平方=16考点难度思路25If x4 + y4 = 100, then the greatest possible value of x is between(A) 0 and 3(B) 3 and 6(C) 6 and 9(D) 9 and 12(E) 12 and 15B基本数论2因为Y 四次方大于等于0考点难度思路那么使得X 最大 则让Y 为0此时X 的四次方要小于100试数即可12

22、：留学资讯26In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could

23、 be(A) 3 and 15(B) 3 and 20(C) 4 and 13(D) 4 and 14(E) 5 and 14C基本数论2抽出的数要乘以（次数+1）即 N*(N+1)要在 15 到 200 之间 也可以试数得到考点难度思路27For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by.If T is the sum of the first 10 terms in the sequence, then T is(A) greater than 2(B) b

24、etween 1 and 2(C) between 1/2 and 1(D) between 1/4 and 1/2(E) between 1/4D数列 定义新运算3K 取 1 第一项为 1/2 K 取 2 第二项为-1/4 K 取 3 第三项为 1/8 第四项为-1/16 一次类考点难度思路推 前两项计算结果为 1/4 后面 3 与 4 项和为 1/165 和 6 项 1/64 以此类推 可以估算出结果 也可以等比数列求和公式13：留学资讯28Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume.

25、 If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z ?(A) y + 3z(B) (y + z) /4(C) 2y + 3z(D) 3y + z(E) 3y + 4.5zA比例3X+2Y+3Z=1.5(X+Y+Z) 解这个三元一次不定方程 将 X 放在等

26、号一边 Y 和 Z 挪到另一考点难度思路边即可29A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many d

27、ifferent stocks is it possible to uniquely designate with these codes?(A)(B)(C)(D)(E)2,9518,12515,60016,30218,278E排列组合3一个字母的 26 种考点难度思路两个字母因为可以一样 262 三个字母 263 算出三种情况的数量加起来14：留学资讯30Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additiona

28、l machines, each working at the same constant rate, will be needed to complete the job in 8 days?(A) 2(B) 3(C) 4(D) 6(E) 8B工作问题 比例2工作总量=效率*时间 6 台考点难度思路做12 天 总量为1 那么每台每天的效率为172所以 8 天做完 需要每天的工作量为 1/9 则一共需要 9 台 比之前多 3 台31All of the stocks on the over-the-counter market are designated by either a 4-lett

29、er or a 5-letter code that is created by using the 26 letters of the alphabet.Which of the followinggives theum number of different stocks that can be designated with these codes?(A) 2(265)(B) 26(264)(C) 27(264)(D) 26(265)(E) 27(265)C排列组合34 个字母的考点难度思路因为可以重复字母 所以为 264 5 个字母的情况为 265两种情况的数字相加提取公因数 找到15

30、：留学资讯32Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25.Each pot cost$0.25 more than the next one below it in size.What was the cost, in dollars, of the largest pot?(A) $1.75(B) $1.85(C) $2.00(D) $2 15(E) $2 30C等差数列2把最大的设为 X 其余一次减少 0.25 第 6 项为 X-1.25 和为 8.25 求出 X考点难度思路3

31、3A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?(A)(B)(C)(D)(E)162426303232排列组合4先从 4 对夫妻中选 3 对出来 因为不能选同一对的 所以最终一定是来自 3 对不同夫妻考点难度思路里的人 顺

32、序不影响结果 于是 4C3 选出来的 3 对夫妻 每对再选出 1 个人 那么是 23 乘起来一共 32 种情况16：留学资讯34A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior officers and 1 junior officer, how many different committees are possible?(A)(B)(C)(D)(E)8245880210D排列组合26 个

33、S 选 3 个 顺序不影响 6C3 4 个 J 选 1 个 4C1 乘起来得出考点难度思路35While working alone at their respective constant rates, computer X processes 240 files in 4 hours and computer Y processes 240 files in 8 hours. If all files processed by these computers are the same size, how long would it take the two computers, worki

34、ng at the same time and at their respective constant rates, to process a total of 240 files?(A) 2 hr(B) 2 hr 20 min(C) 2 hr 40 min(D) 6 hr(E) 6 hr 20 minC工作问题3X 的效率为 60/H Y 效率是 30/H考点难度思路合起来速度 90 240 除以 90 算出17：留学资讯36If x 0, then(A) -1(B) 0(C) 1(D) x(E) |x| / xE绝对值2分类讨论 X 大于和小于 0 的情况考点难度思路得出37is bet

35、ween(A) 300 and 400(B) 400 and 500(C) 500 and 600(D) 600 and 700(E) 700 and 800E基本数论1试数即可考点难度思路18：留学资讯38A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other

36、 district. What is the minimum possible population that the least populated district could have?(A) 10,700(B) 10,800(C) 10 900(D) 11 000(E) 11,100D比例4要找最小值 那么使得其余 10 个 city 的值尽量大考点难度思路但是最大只能是最小的 1.1 倍 所以另外 10 个city 是最小值的一共 11 倍加上最小值city一共 12 倍132000 除以 12 得出39Which of the following is an integer?(A)

37、 I only(B) II only(C) III only(D) I andonly(E) I, II, and IIIE分数小数21 和2考点难度思路都是分母的倍数可直接看出重点看3 12！除以7！以后还剩下12*11*10*9*8还可以被 5！整除 所以 3 个均为整数19：留学资讯40Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per mi

38、nute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?(A) 6(B) 8(C) 10(D) 12(E) 15D比例2每分钟 Q 比 P 多 30 现在问多 6 是 1/5 分钟 即 12 秒考点难度思路41Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fo

39、urth theater ticket with a price of $16, what is the average price of all 4 theater tickets?(A) $4(B) $6(C) $8(D) $10(E) $12D平均数28*3+16=40考点难度思路再除以 420：留学资讯42An auction house charges a commission of 15 percent on the first $50,000 of the sale price of an item, plus 10 percent on the amount of the sa

40、le price in excess of $50,000. What was the sale price of a painting for which the auction house charged a total commission of$24,000 ? (A) $115,000 (B) $160,000 (C) $215,000 (D) $240,000(E) $365,000C比例350000*15%+(X-50000)*10%=24000 解出 X考点难度思路43Which of the following inequalities has a solution set

41、that, when graphed on the number line, is a single line segment of finite length?(A)X4 1(B)X3 27(C)X2 16(D)2 |X| 5(E)2 3X + 4 6E考点 不等式难度 3思路 分别解出不等式符合要求或者数形结合的思路 前四个要么是两段要么是射线 只有最后一个21：留学资讯44A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the sa

42、me tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?(A) 1/4(B) 1/3(C) 2/5(D) 5/4(E) 3/2C工作问题2考点难度思路小速度为 1/2 大速度为 2 速度和 5/2 所以时间为 2/545In the graduating class of acertain college, 48 percent of the

43、 students are male and 52percent are female.In this class 40 percent of the male and 20 percent of the femalestudents are 25 years old or older.If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? (A) 0.90(B

44、) 0.70(C) 0.45(D) 0.30(E) 0.25B集合3考点难度思路48%里的 40% 相乘得 19.2%的且大于等于 25 岁 女性 52%里的 20% 相乘得10.4%的女性且大于等于 25 岁 那么小于 25 约等于 70%22：留学资讯46In the figure above, points P and Q lie on the circle with center O.What is the value of s ?(A)(B)(C)(D)(E)1/21232/2B考点难度思路几何 圆 直角三角形3分别从 P 和 Q 点做 X 轴垂线 角 POQ 是直角 左右分别为 3

45、0 60 和 60 30 度角 即可算出坐标47As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around twocircular wheels each 1 foot in diameter.What is the distance, in feet, between the centers of the two wheels?(A)(B)(C)(D)(E)(15 - ) / 25/415 - 215 -2A平面几何2总长度减去一个完整的圆 再除以 2考点难度思路23：留学资讯

46、48For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ?(A) f(x) = x 2(B) f(x) = x + 1(C) f(x) = x(D) f(x) = 2/x(E) f(x) = -3xE定义新运算3把选项中的 X 换成 a 和 b 分别代入 再代入 a+b 看看是否完全一致即可考点难度思路49If in a certain population, people are born at an average rate of 9 people e

47、very 2 seconds and people die at an average rate of 3 people every 2 seconds by approximately how many people does the population increase in 1 day?(A)(B)(C)(D)(E)17,28025,920129,600259,200388,800D比例31 天 24 小时 每小时 60 分钟 每分钟 60 秒 所以一天是 86400 秒 每 2 秒增加 9 人减考点难度思路少 3 人 差值为 6 所以每秒增加 3 人 86400*3 得出50For

48、how many integers n is= n2 ?(A) None(B) One(C) Two(D) Three(E) More than three2nC指数运算和函数方程3可以数形结合看出 也可以代数计算 只有 2 和 4 两个整数解 还有一个解为负 不是整考点难度思路数 需要考虑到24：留学资讯51The manager of a theater noted that for every 10 admission tickets sold, the theater sells 3 bags of popcorn at $2.25 each, 4 sodas at $1.50 eac

49、h, and 2 candy bars at $1.00 each. To the nearest cent, what is the average (arithmetic mean) amount of these snack sales per ticket sold?(A) $1.48(B) $1.58(C) $1.60(D) $1 64(E) $1 70A方程2每 10 张票可售出 3 个 P 4 个 S 以及 2 个 C 加和为 14.75 除以 10 约等于 A 选项考点难度思路52The number 75 can be written as the sum of the sq

50、uares of 3 different positive integers. What is the sum of these 3 integers?(A) 17(B) 16(C) 15(D) 14(E) 13E质数375 为 3 个整数的平方之和考点难度思路试数即可从最大值为 8 依次减小 试出为 7 5 125：留学资讯53The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps, the ra

51、tio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?(A) 20(B) 30(C) 40(D) 60(E) 90C方程3设 K 的数量 X A 的数量为 Y 则列出方程组 3x=5y 和 5(x-10)=7(y+10) 解方程即可考点难度思路54The perimeters of square region S and rectangular region R are equal.I

52、f the sides of R are in the ratio 2 : 3, what is the ratio of the area of region R to the area of region S ?(A)(B)(C)(D)(E)25 : 1624 : 255 : 64 : 54 : 9B平面几何 比例3长宽设为 2X 与 3X考点难度思路则正方形边长为 2.5X 那么分别算出面积即可26：留学资讯55On July 1 of last year, the total number of employees at Company E was decreased by 10 pe

53、rcent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in number of employees than before the decrease. The total of the combined salaries of all of the employees at Company E after July 1 last year was what percent of that before July 1 last year?(A)