【小站教育】GMAT数学笔记(5)

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(D)Ⅲ only (E) Ⅰand Ⅲ

<3> What is the greatest prime factor of 2100 - 296? (A) 2

(B) 3

(C) 5

(D) 7

(E) 11

<4> A positive integer n is said to be “prime-saturated” if the product of all the different

positive prime factors of n is less than the square root of n. What is the greatest two-digit

prime-saturated integer?

(A) 99 (B) 98 (C) 97 (D) 96 (E) 95

<5> If 1050 – 74 is written as an integer in base 10 notation, what is the sum of the digits in

that integer?

（A）424 （B）433 （C）440 (D) 449 (E) 467

<6> If P and Q are different points in a plane, the set of all points in this plane that are closer to P than to Q is

(A) the region of the plane on one side of a line (A) the interior of a square

(B) a wedge-shaped region of the plane

(C) the region of the plane bounded by a parabola (D) the interior of a circle

<7> A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change? (A)Ⅰonly Ⅱ,and Ⅲ

(B) Ⅱonly

(C) Ⅰand Ⅱonly

(D) Ⅱand Ⅲ only (E) Ⅰ,

<8> Test y physics biology history chemistry math

onya's score 90 96 89 88 80 Mean score 84 86 81 85 88 tandard deviation 2 5 4 3 4 Th e cha rt abo

ve shows data for five tests that Sonya took. On which of the five tests did she

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score highest relative to the rest of the test takers?

(A) math (B) biology (C) physics (D) history (E) chemistry <9> Some people in New York express 2/8 as 8th Feb and others express 2/8 as 2nd Aug. This can be confusing as when we see 2/8, we don’t know whether it is 8th Feb or 2nd Aug. However, it is easy to understand 9/22 or 22/9 as 22nd Sept, because there are only 12 months in a year. How many dates in a year can cause this confusion?

（A）48 （B) 53 （C）120 （D）132 （E）144

<10> Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of 1ast year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2600, what was the range of the monthly closing balances of Carl's account last year?

(1) Last year the closing balance of Carl's account for April was less than $2625. (2) Last year the closing balance of Carl's account for June was less than $2675. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

<11> At the beginning of a five-day trading week, the price of a certain stock was $10 per share. During the week, four of the five closing prices of the stock exceeded $10. Did the average closing price of the stock during the week exceed its price at the beginning of the week?

(1) The stock's closing price on Tuesday was the same as its closing price on Thursday. (2) The sum of the stock's highest and lowest closing prices during the week was 20. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

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<12> 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

<13> 三人独立地去破译一个密码，他们能译出的概率分别为 1/5,1/3,1/4, 求此密 码被译出的概率。

<14> 某市共有 10000 辆自行车，其牌照号码从 00001 到 10000，求偶然遇到的 一辆自行车，其牌照号码中有数字 8 的概率。 <15> 用 0,2,4,6,9 这五个数字可以组成数字不重复的五位偶数共有多少个？ <16>有 5 个队伍参加了足球联赛，任意两队之间都要进行主客场各一场比赛，问总 共将有多少场比赛？

<17> 甲，乙，丙，丁，戊五人并排站成一排，如果乙必须站在甲的右边（甲乙可 以不相邻），那么不同的排法共有多少种？ <18> 4 本不同的书分给 2 人，每人 2 本，不同的分法有多少种？

<19> 两把 keys,放到有 5 个 keys 的 keychain 中，相邻的概率为多少(分直线和环 形)？

<20> 6 张同排连号的电影票，分给 3 名男生和 3 名女生，如欲男女相间而坐，则

不同的分法数为多少？ <21> 有 4 对人，从中取 3 个人，不能从任意一对中取 2 个，问有多少种取法？ <22> 从 6 双不同的手套中任取 4 只，求其中恰有一双配对的概率。 <23> 3 封不同的信，有 4 个信箱可供投递，共有多少种投信的方法？ <24> 3 个打字员为 4 家公司服务，现在每家公司各有 1 份文件需要录入，问每个打 字员都收到文件的概率？

<25> A 发生的概率是 0.6，B 发生的概率是 0.5，问 A,B 都不发生的最大概率？ <26> 袋中有 a 只白球，b 只红球，依次将球一只只摸出，不放回。求第 k 次摸出 的是个白球的概率（1≤k≤a+b）。 <27> 掷一枚均匀硬币 2n 次，求出现正面 k 次的概率。

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<28> 有 4 组人，每组一男一女，从每组各取一人，问取出两男两女的概率？

<29> A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars? （A）0 （B）1/9（C）2/9 （D）1/3（E）1

<30>A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

（A）1/12 （B）1/6 （C）1/5 （D）1/3 （E）1/2

<31> If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?

（A）20 （B）40 （C）50 （D）80 （E）120

<32> How many seven-digit numbers contain the digit '7' at least once? <33> In how many ways can seven students A, B, C, D, E, F and G line up in one row if students B and C are always next to each other?

<34> There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

(A)20 (B) 25 (C) 40 (D) 60 (E) 125

<35> How many different 6-letter sequences are there that consist of 1 A, 2 B’s, and 3 C’s ?

(A)6 (B) 60 (C) 120 (D) 360 (E) 720

<36> In how many distinguishable ways can the seven letters in the word MINIMUM be arranged, if all the letters are used each time? (A) 7 (B) 42 (C) 420 (D) 840 (E)5040

<37> A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second

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row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?

(A)S

(B) 6 (C) 9 (D) 24 (E)36

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