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GMAT Quantitative The University of Nottingham 2017

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; Subject: ; Class: ; with 37 questions; test in 75 minutes; update 26/07/2017
Time 75 minutes
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Subjects Update 26/07/2017
Class Number of questions 37
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Question 1.

If the square root of p2 is an integer, which of the following must be true?

  1. p2 has an odd number of factors
  2. p2 can be expressed as the product of an even number of prime factors
  3. p has an even number of factors
(A)

I

(B)

II

(C)

III

(D)

I and II

(E)

II and III

Question 2.

The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the value of n?

(A)

6

(B)

8

(C)

9

(D)

12

(E)

15

Question 3.

How many factors does 362 have?

(A)

2

(B)

8

(C)

24

(D)

25

(E)

26

Question 4.

In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?

(A)

1

(B)

2

(C)

3

(D)

4

(E)

5

Question 5.

For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y?

(A)

5

(B)

6

(C)

15

(D)

16

(E)

18

Question 6.

a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A)

16

(B)

13

(C)

5

(D)

3

(E)

none of the above

Question 7.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

(A)

5                

(B)

5(x – y)

(C)

20x

(D)

20y

(E)

35x

Question 8.

For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are four- digit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?

(A)

2000

(B)

200

(C)

25

(D)

20

(E)

2

Question 9.

A restaurant pays a seafood distributor d dollars for 6 pounds of Maine lobster. Each pound can make v vats of lobster bisque, and each vat makes b bowls of lobster bisque. If the cost of the lobster per bowl is an integer, and if v and b are different prime integers, then which of the following is the smallest possible value of d?

(A)

15

(B)

24

(C)

36

(D)

54

(E)

90

Question 10.

If p3 is divisible by 80, then the positive integer p must have at least how many distinct factors? 

(A)

2

(B)

3

(C)

6

(D)

8

(E)

10

Question 11.

Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

(A)

140

(B)

210

(C)

1400

(D)

2100

(E)

3500

Question 12.

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5a2b7c3d ÷ 5p2q7r3s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A)

16

(B)

20

(C)

25

(D)

40

(E)

It cannot be determined from the information given

Question 13.

How many numbers that are not divisible by 6 divide evenly into 264,600?

(A)

9

(B)

36

(C)

51

(D)

63

(E)

72

Question 14.

f the prime factorization of the integer q can be expressed as a2x.bx.c3x-1, where a, b, c, and x are distinct positive integers, which of the following could be the total number of factors of q?

(A)

3j + 4, where j is a positive integer

(B)

5k + 5, where k is a positive integer

(C)

6l + 2, where l is a positive integer

(D)

9m + 7, where m is a positive integer

(E)

10n + 1, where n is a positive integer

Question 15.

Which of the following is the lowest positive integer that is divisible by 8, 9, 10, 11, and 12?

(A)

7,920

(B)

5,940

(C)

3,960

(D)

2,970

(E)

890

Question 16.

h(n) is the product of the even numbers from 2 to n, inclusive, and p is the least prime factor of h(100)+1. What is the range of p?

(A)

< 40

(B)

< 30

(C)

> 40

(D)

< 10

(E)

Indeterminate

Question 17.

The function f is defined for all positive integers n by the following rule. f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p)=

(A)

p-1

(B)

p-2 

(C)

(p+1)/2

(D)

(p-1)/2

(E)

2

Question 18.

For any positive integer n, the length of n is defined as number of prime factors whose product is n, For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?

(A)

0

(B)

1

(C)

2

(D)

3

(E)

4

Question 19.

if n is a positive integer less than 200 and 14n/60 is an integer, then n has how many different positive prime factors?

(A)

two

(B)

three

(C)

five

(D)

six

(E)

eight

Question 20.

If x is an integer, then x(x – 1)(x kmust be evenly divisible by three when k is any of the following  values EXCEPT

(A)

-4 

(B)

-2

(C)

-1

(D)

2

(E)

5

Question 21.

a, b, c, and d are consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =

(A)

2

(B)

6

(C)

12

(D)

20

(E)

30

Question 22.

How many integers are there between 51 and 107, inclusive?

(A)

51

(B)

55

(C)

56

(D)

57

(E)

58

Question 23.

a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?

(A)

x = 2; y = 6

(B)

x = 3; y = 6

(C)

x = 7; y = 9

(D)

x = 10; y = 4

(E)

x = 10; y = 7

Question 24.

Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?

   abdc

+ dbca

(A)

3689 

(B)

6887

(C)

8581

(D)

9459

(E)

16091

Question 25.

8k8

+ k88

1,6p6

If k and p represent non-zero digits within the integers above, what is p?

(A)

6

(B)

7

(C)

8

(D)

9

(E)

17

Question 26.

If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?

(A)

3

(B)

6

(C)

11

(D)

22

(E)

222

Question 27.

2 2

a 3

+ 4 b

9 0

If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ba?

(A)

10

(B)

15

(C)

25

(D)

51

(E)

52

Question 28.

2 2

a 3

+ 4 b

9 0

If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ba?

(A)

10

(B)

15

(C)

25

(D)

51

(E)

52

Question 29.

If the 4 x 4 grid pictured at right is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?

(A)

124

(B)

153

(C)

178

(D)

192

(E)

214

Question 30.

What is the value of a + b?

(A)

30

(B)

50

(C)

55

(D)

65

(E)

90

Question 31.

If l1 is parallel to l2, what is x + 2y?

(A)

90

(B)

120

(C)

180

(D)

270

(E)

360

Question 32.

What is the value of a + b + c + d + e + f?

(A)

180

(B)

270

(C)

300

(D)

360

(E)

720

Question 33.

In triangle ABC, if BC = 3 and AC = 4, then what is the length of segment CD?

(A)

3

(B)

15/4

(C)

5

(D)

16/3

(E)

20/3

Question 34.

The figure is comprised of three squares and a triangle. If the areas marked X, Y and Z are 25, 144, and 169, respectively, what is the area of the triangle marked T?

(A)

25

(B)

30

(C)

50

(D)

60

(E)

97

Question 35.

If BE || CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?

(A)

12

(B)

18

(C)

24

(D)

30

(E)

48

Question 36.

In the diagram, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?

(A)

3/2

(B)

7/4

(C)

15/8

(D)

16/9

(E)

2

Question 37.

Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I.  3       II. 9√3        III. 13.5

(A)

I only

(B)

II only

(C)

III only

(D)

II and III

(E)

I, II and III

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30    Question 31    Question 32    Question 33    Question 34    Question 35    Question 36    Question 37   
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