# GMAT Quantitative The University of Manchester 2017

Subject: ; Class: ; with 37 questions; test in 75 minutes; update 26/07/2017
 Time 75 minutes Time to take the test Start exam Click button start to test. Guide to the test Subjects Gmat test Update 26/07/2017 Class Level 3 Number of questions 37 View 712 Tested 0

Question 1.

If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

 (A) 1,800 (B) 1,845 (C) 1,890 (D) 1,968 (E) 2,016

Question 2.

In an increasing sequence of 5 consecutive even integers, the sum of the second, third, and fourth integer is 132. What is the sum of the first and last integers?

 (A) 84 (B) 86 (C) 88 (D) 90 (E) 92

Question 3.

What is the sum of the multiples of 7 from 84 to 140, inclusive?

 (A) 896 (B) 963 (C) 1008 (D) 1792 (E) 2016

Question 4.

If each term in the sum a1 + a2 + a3 + ... +an is either 7 or 77 and the sum is equal to 350, which of the following could equal to n?

 (A) 38 (B) 39 (C) 40 (D) 41 (E) 42

Question 5.

For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)(k+1)] × (1 / 2k). If T is the sum of the first 10 terms of the sequence, then T is:

 (A) greater than 2 (B) between 1 and 2 (C) between 1/2 and 1 (D) between 1/4 and 1/2 (E) less than 1/4

Question 6.

S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

 (A) 1 (B) 2 (C) 4 (D) 6 (E) 9

Question 7.

Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 – S9

 (A) 2 (B) 120 (C) 128 (D) 250 (E) 256

Question 8.

Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 = 316, what is the first value of n for whichQn is an integer?

 (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Question 9.

What is the sixtieth term in the following sequence?    1, 2, 4, 7, 11, 16, 22...

 (A) 1,671 (B) 1,760 (C) 1,761 (D) 1,771 (E) 1,821

Question 10.

Sequence S is defined as Sn = X + (1/X), where X = Sn – 1 + 1, for all n > 1. If S1= 201, then which of the following must be true of Q, the sum of the first 50 terms of S?

 (A) 13,000 < Q < 14,000 (B) 12,000 < Q < 13,000 (C) 11,000 < Q < 12,000 (D) 10,000 < Q < 11,000 (E) 9,000 < Q < 10,000

Question 11.

In a certain sequence, every term after the first is determined by multiplying the previous term by an integer constant greater than 1. If the fifth term of the sequence is less than 1000, what is the maximum number of nonnegative integer values possible for the first term?

 (A) 60 (B) 61 (C) 62 (D) 63 (E) 64

Question 12.

The sum of the squares of the first 15 positive integers (12 + 22 + 32 + . . . + 152) is equal to 1240. What is the sum of the squares of the second 15 positive integers (162 + 172 + 182 + . . . + 302) ?

 (A) 2480 (B) 3490 (C) 6785 (D) 8215 (E) 9255

Question 13.

The infinite sequence Sk is defined as Sk = 10 Sk – 1 + k, for all k > 1. The infinite sequence An is defined as An = 10 An – 1 + (A1 – (n - 1)), for all n > 1. q is the sum of Sk and An. If S1 = 1 and A1 = 9, and if An is positive, what is the maximum value of k + n when the sum of the digits of q is equal to 9?

 (A) 6 (B) 9 (C) 12 (D) 16 (E) 18

Question 14.

A certain club has exactly 5 new members  at the  end of its first week.  Every  subsequent week, each of the previous week's new members (and only these members) brings exactly x new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?

 (A) $$\sqrt[12]{5}$$ (B) 311 511 (C) 312 512 (D) 311 512 (E) 6012

Question 15.

362  + 372 + 382 + 392  + 402 + 412 + 422 + 432 + 442      =

 (A) 14400 (B) 14440 (C) 14460 (D) 14500 (E) 14520

Question 16.

A certain established organization has exactly 4096 members. A certain new organization has exactly 4 members. Every 5 months the membership of the established organization increases by 100 percent. Every 10 months the membership of the new organization increases by 700 percent. New members join the organizations only on the last day of each 5- or 10-month period. Assuming that no member leaves the organizations, after how many months will the two groups have exactly the same number of members?

 (A) 20 (B) 40 (C) 50 (D) 80 (E) 100

Question 17.

In the infinite sequence A, An = xn-1 + xn + xn+1 + xn+2 + xn+3, where x is a positive integer constant. For what value of n is the ratio of An to x(1 + x(1 + x(1 + x(1 + x)))) equal to x5?

 (A) 8 (B) 7 (C) 6 (D) 5 (E) 4

Question 18.

What is the sum of the even integers between 200 and 400, inclusive?

 (A) 29,700 (B) 30,000 (C) 30,300 (D) 60,000 (E) 60,300

Question 19.

 98 -200 310 -396 498 102 -202 290 -402 502 101 -198 305 -398 501 100 -204 295 -404 500 99 -196 300 -400 499

What is the sum of all of the integers in the chart above?

 (A) 0 (B) 300 (C) 500 (D) 1,500 (E) 6,500

Question 20.

The sequence f(n) = (2n)! ÷ n! is defined for all positive integer values of n. If x is defined as the product of the first 10 ten terms of this sequence, which of the following is the greatest factor of x?

 (A) 220 (B) 230 (C) 245 (D) 252 (E) 255

Question 21.

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

 (A) 0 (B) 1 (C) 3 (D) 4 (E) 6

Question 22.

If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

 (A) 8 (B) 9 (C) 16 (D) 23 (E) 24

Question 23.

If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of $$\sqrt{288kx}$$ ?

 (A) 24k√3 (B) 24√k (C) 24√(3k) (D) 24√(6k) (E) 72√k

Question 24.

1025 – 560 is divisible by all of the following EXCEPT:

 (A) 11 (B) 8 (C) 5 (D) 4 (E) 3

Question 25.

x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?

 (A) 24 (B) 21 (C) 20 (D) 17 (E) 15

Question 26.

When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I.  15.15    II.  18.16    III. 17.17

 (A) I only (B) II only (C) III only (D) I and II only (E) I and III only

Question 27.

The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each child at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday party do not eat anything. If the number of cupcakes that remain uneaten is less than the number of children at the birthday party, what must be true about the number of uneaten cupcakes?
I. It is a multiple of 2.    II. It is a multiple of 3.  III. It is a multiple of 7.

 (A) I only (B) II only (C) III only (D) I and II only (E) I, II and III

Question 28.

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

 (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Question 29.

A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?

 (A) 33 (B) 46 (C) 49 (D) 53 (E) 86

Question 30.

When x is divided by 4, the quotient is y and the remainder is 1. When x is divided by 7, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

 (A) (4z/7) + 5 (B) (7z + 5)/6 (C) (6z + 7)/4 (D) (7z + 5)/4 (E) (4z + 6)/7

Question 31.

If n is an integer and n4 is divisible by 32, which of the following could be the remainder when n is divided by 32?

 (A) 2 (B) 4 (C) 5 (D) 6 (E) 10

Question 32.

x1 and x2 are each positive integers. When x1 is divided by 3, the remainder is 1, and when x2 is divided by 12, the remainder is 4. If y = 2x1 + x2, then what must be true about y?

I.   y is even                II.  y is odd                 III. y is divisible by 3

 (A) I only (B) II only (C) III only (D) I and III only (E) II and III only

Question 33.

The sum of all the digits of the positive integer q is equal to the three-digit number x13. If q = 10n – 49, what is the value of n?

 (A) 24 (B) 25 (C) 26 (D) 27 (E) 28

Question 34.

If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?

 (A) 8 (B) 12 (C) 18 (D) 24 (E) 48

Question 35.

Susie can buy apples from two stores: a supermarket that sells apples only in bundles of 4, and a convenience store that sells single, unbundled apples. If Susie wants to ensure that the total number of apples she buys is a multiple of 5, what is the minimum number of apples she must buy from the convenience store?

 (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Question 36.

Each of the following numbers has a remainder of 2 when divided by 11 except:

 (A) 2 (B) 13 (C) 24 (D) 57 (E) 185

Question 37.

If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 – 12n ?

 (A) - 11 (B) - 1 (C) 0 (D) 1 (E) 11