GRE - QUANT - NUMBERS - DIVISBILITY

1)n is an even integer and a multiple of 3.

Column A:  The remainder when n is divided by 12        Column B: 6                                        

2) If n is the integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

(A) (B)               (C)       (D)    (E)

3)               Column A: The remainder when 48 is divided by 5  

 Column B: The remainder when 48 is divided by 7

4) If n =15×28×26, which of the following is NOT an integer?

(A)      (B)                 (C)     (D)      (E)

5)x,y,z are positive integers and   .

Column A: The remainder when z is divided by x

Column B: The remainder when z is divided by y

6) When a certain number is divided by 7, the remainder is0. If the remainder in not 0 when the number is divided by 14, then the remainder must be

(A)  1                             (B)     2              (C)      4        (D)       6           (E)    7

8)x is an integer

                                                 The remainder when 2x is divided by4 is 0

Column A: The remainder when x is divided by 4                             Column B: 0

9) If integer x were divided by 7, the quotient would be 12 with a remainder of 1. Therefore, x equals

(A)  91          (B) 90         (C) 88             (D) 85          (E)   83 

10) If the remainder is 1when the integer n is divided by 15, what is the remainder when n is divided by 5?

(A)   1     (B)   2     (C) 3 (D) 4      (E) It cannot be determined from the information given

11) n is a positive integer

Column A: The remainder when n(n+1) is divided by 2                     Column B:  1

 12) Each of the following numbers have two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an integer?

(A)25□, □06        (B)50□,□26               (C)56□,□02      (D)62□,□50      (E)65□,□20

13)                                     When integer n is divided by 9, the remainder is 2

Column A: The remainder when is divided by3                                    Column B: 2

14) What is the remainder when   is divided by 8?

(A) 5            (B) 3          (C) 2               (D) 1                 (E)0

15) Column A: The remainder when a positive odd integer is divided by 2

Column B:  The remainder when a positive even integer is divided by 2

16) The number  is divisible by all of the following except

(A) 250             (B) 125       (C) 32            (D) 16           (E) 6

17)  When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by9?

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

18) 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

19) If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of 24 ?

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

20) 10²⁵-500 is divisible by all of the following EXCEPT

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

21)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

22) 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 ?

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

23) 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

24) 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

25) 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)  + 5(B) (C) (D) (E)

26) and  are each positive integers. When  is divided by 3, the remainder is 1, and when  is divided by 12, the remainder is 4. If y = 2 + , 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

28) 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

29) 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

30) 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

31) 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

32) 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. What is the value of y in terms of z?

34)The number m yields a remainder p when divided by 14 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of m?

(A) 45              (B) 53              (C) 72              (D) 85

35)The remainder when x + 7 divided by 3 is 2
Column A: The remainder when x is divided by 2 is              Column B: 0

36) The maximum remainder when 50 is divided by a positive integer less than 50 is

37)  Remainder when  is divided by 28.

38) The remainder when n is divided by 3 is 1, and the remainder when n+1 is divided by 2 is 1.
Column A: The remainder when n-1 is divided by 6              Column B: 3

39)The term  is not divisible by which of the following.

(A) 4                (B) 6                (C) 8                (D) 10

40) If   n = +  +  + ....+ . What is the remainder ,when n is divided by 14 ?

41)  n is an even integer

 Column A:  The remainder when n is divided by 3

  Column B:  The remainder when n is divided by 5

42)z= - + -123. If z is divided by 122, What is the remainder?

43) If x, y, z each is divisible by 7 and remainder is 3, then  the remainder when x+y+z is

divided by 7.

44)Column A: Numbers between 1 to 50 inclusive that are divisible by 3
Column B: Numbers between 51 to 100 inclusive that is divisible by 3

45)n is number. When n divide by 7 it gives the remainder of 3.Then find the remainder when -5 is divide by the 7
A)2                   B)4                   C)6                   D)8                  E)10

46) A number, when divided by 3, leaves a remainder 1. When the same number divided by 15 leaves the remainder 13?
(A) 15              (B) 27                          (C) 35                          (D) 43  (E)68

47)  + 4 is divisible by 5 find the value of n
A) 23                B) 24                C) 25                D) 26               E) 27

48)                   n is divisible by 17 and  13
Column A: n           Column B:442

49)Column A: Numbers divisible by 3 between 1 to 50
Column B: Numbers divisible by 3 between 51 to 100

50)  If x is divided by 7, the remainder is 3, then the remainder of  2x-1 when divided by 7.

51)                            If x is divided by 5, the remainder is 3
Column A: divided by 5,remainder isColumn B:  4

52) If n is divided by 12, the remainder is 5.What is remainder, when  is divided by 8.

53) If k and n is divided by 9, the remainders are 2 and 5 respectively. K >n and if k-n is divided by 9, then what is the reminder.

55)x+5 when divided by 3 leaves a remainder 2..

Column A: remainder when x is divided by 2             Column B: 1

56) If a number x leaves remainder 7 when divided by 11 and leaves remainder 1 when divided by 5, then 
Column A: Least possible value of x Column B: 40 

57)  n is an integer

14ⁿ is divisible by 32
Column A: n                                        Column B: 4

58) If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?
Select ALL such statements.

(A) n is odd                                                      (B) n + 1 cannot be a prime number 

(C) (n + 2) divided by 7 has remainder 2                    (D) n + 3 is divisible by 5

59)n is a positive integer

 p = 8 x 9 x 11 x n

Column A: The remainder when p is divided by 6

Column B: The remainder when p is divided by 33

60.  x is a positive number, when  divided by 9 leaves a remainder 2.  n is a positive integer when divided by 9 leaves a remainder 5. x >  n. The remainder when x-n is divided by 9 is

61. k is a positive integer. The function f(x) is defined as f(x) is the remainder when x is divided by k.  The value of k, if f(k+25)=3 is