#### 2018年GMAT年度回顾——数学｜沃邦年终总结 ### 1. 数论

GMAT 数学中会出现一些涉及数论的题目，尽管其中仅仅要求运用最为基本的数论定理，但往往它们也足以对考生造成不小的困扰。

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x+y?
A. 6
B. 9
C. 10
D. 11
E. 14

If x and y are positive integers such that y is a multiple of 5 and 3x+2y=200, then x must be a multiple of which of the following?
A. 3
B. 6
C. 7
D. 8
E. 10

If k is a positive integer, what is the remainder when (k+2)(k^3-k) is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4

If n=20!+17, then n is divisible by which of the following?
I. 15
II. 17
III. 19
A. None
B. I only
C. II only
D. I and II
E. II and III

If n is an integer greater than 6, which of the following must be divisible by 3?
A. n(n+1)(n-4)
B. n(n+2)(n-1)
C. n(n+3)(n-5)
D. n(n+4)(n-2)
E. n(n+5)(n-6)

If n is a positive integer and the product of all the integers from 1 to n, inclusive, is divisible by 990, what is the least possible value of n?
A. 8
B. 9
C. 10
D. 11
E. 12

When positive integer x is divided by positive integer y, the remainder is 9. If x/y=96.12, what is the value of y?
A. 96
B. 75
C. 48
D. 25
E. 12

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18

If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be
A. 2
B. 5
C. 6
D. 7
E. 14

If n=33^43+43^33, what is the units digit of n?
A. 0
B. 2
C. 4
D. 6
E. 8

If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?
A. One
B. Two
C. Three
D. Seven
E. Ten

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
A. 3
B. 4
C. 5
D. 6
E. 7

If n is a positive integer, for which of the following values of k i 25*10^n+k*10^2n divisible by 9?
A. 9
B. 16
C. 23
D. 35
E. 47

What is the remainder when 3^24 is divisible by 5?
A. 0
B. 1
C. 2
D. 3
E. 4

A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. If k is a perfect number, what is the sum of the reciprocals of all the positive factors of k?
A. 1/4
B. 56/27
C. 2
D. 3
E. 4

For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2*4*6*8*10*12. What is the greatest prime factor of f(24)?
A. 23
B. 19
C. 17
D. 13
E. 11

The function f is defined for each positive three-digit integer n by f(n)=(2^x)(3^y)(5^z), where x, y, and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), then m-v=
A. 8
B. 9
C. 18
D. 20
E. 80

If 10^50-74 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

If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
A. 6
B. 12
C. 24
D. 36
E. 48

### 2. 集合的容斥原理

GMAT 数学中涉及集合的难题主要在于容斥原理的应用。

Of the 150 houses in a certain development, 60 percent have air-conditioning , 50 percent have a sunporch, and 30 percent have a swimming pool. If 5 of the houses have all three of these amenities and 5 have none of them, how many of the houses have exactly two of these amenities?
A. 10
B. 45
C. 50
D. 55
E. 65

### 3. 排列组合

GMAT 数学中也会出现排列组合问题，而它们常常就会给考生带来相当大的挑战。

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 book approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?
A. 6
B. 40
C. 210
D. 5040
E. 151200

A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
A. 144
B. 152
C. 160
D. 168
E. 176

Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to line up male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?
A. 9
B. 12
C. 15
D. 36
E. 720

The letters D, G, I, I and T can be used to form 5-letter strings such as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurences of the letter I are separated by at least one other letter?
A. 12
B. 18
C. 24
D. 36
E. 48

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
A. 42
B. 70
C. 140
D. 165
E. 315

How many subsets of the set {w, x, y, z} contain w?
A. Four
B. Five
C. Seven
D. Eight
E. Sixteen

There are 5 cars to the 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

There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of the 5 books from the shelf contain at least one paperback and at least one hardback?
A. 75
B. 120
C. 210
D. 246
E. 252

### 4. 概率与统计

GMAT 数学涉及的概率及统计问题对于没接触过统计课的考生来说，或会造成一点困难。

In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
A. 1/6
B. 2/9
C. 6/11
D. 9/16
E. 3/4

For each student in a certain class, a teacher adjusted the student’s test score using the formula y=0.8x+20, where x is the student’s original test score and y is the student’s adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?
A. 12
B. 16
C. 28
D. 36
E. 40

The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
E. 12/25

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m+d?
A. 16%
B. 32%
C. 48%
D. 84%
E. 92%

A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?
A. 3/8
B. 1/4
C. 3/16
D. 1/8
E. 1/16

### 5. 数据充分性

If x and y are positive integers, what is the remainder when 10^x+y is divided by 3?
(1) x=5
(2) y=2

If x is a positive integer, is x^0.5 an integer?
(1) (4x)^0.5 is an integer
(2) (3x)^0.5 is not an integer

If a and b are positive integers, what is the value of the product ab?
(1) The least common multiple of a and b is 48.
(2) The greatest common factor of a and b is 4.

Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?
(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

If a, b, and c are consecutive integers and 0<a<b<c, is the product abc a multiple of 8?
(1) The product ac is even.
(2) The product bc is a multiple of 4.

Of a group of 50 households, how many have at least one cat or at least one dog, but not both?
(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.

If x and y are positive integers, is xy even?
(1) x^2+y^2-1 is divisible by 4.
(2) x+y is odd.

Jill has applied for a job with each of the two different companies. What is the probability that she will get the job offer from both companies?
(1) The probability that she will get a job offer from neither company is 0.3.
(2) The probability that she will get a job offer from exactly one of the two companies is 0.5.

A scientist recorded the number of eggs in each of 10 birds’ nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

The range of the numbers in set S is x, and the range of the numbers in set T is y. If all of the numbers in set T are also in set S, is x greater than y?
(1) Set S consists of 7 numbers.
(2) Set T consists of 6 numbers.

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the mean of the 3 numbers?
(1) The range of the 3 numbers is equal to twice the difference between the greatest numbers and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.

If x, y, and z are three-digit positive integers and if x=y+z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
(1) The tens digit of x is equal to the sum of the tens digits of y and z.
(2) The units digit of x is equal to the sum of the units digits of y and z.

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2018年GMAT年度回顾——阅读｜沃邦年终总结

2018年GMAT年度回顾——语法｜沃邦年终总结