Aptitude - Numbers

Exercise :: Numbers - General Questions

61. 

When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?

A. 339
B. 349
C. 369
D. Data inadequate

Answer: Option B

Explanation:

x = 13p + 11 and x = 17q + 9

13p + 11 = 17q + 9

17q - 13p = 2

q = 2 + 13p
17

The least value of p for which q = 2 + 13p is a whole number is p = 26
17

x = (13 x 26 + 11)

   = (338 + 11)

   = 349


62. 

(51 + 52 + 53 + ... + 100) = ?

A. 2525
B. 2975
C. 3225
D. 3775

Answer: Option D

Explanation:

Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)

    = 100 x (1 + 100) - 50 x (1 + 50)
2 2

    = (50 x 101) - (25 x 51)

    = (5050 - 1275)

    = 3775.


63. 

(800 64) x (1296 36) = ?

A. 420
B. 460
C. 500
D. 540
E. None of these

Answer: Option E

Explanation:

Given Exp. = 800 x 1296 = 450
64 36

64. 

Which natural number is nearest to 8485, which is completely divisible by 75 ?

A. 8475
B. 8500
C. 8550
D. 8525
E. None of these

Answer: Option A

Explanation:

On dividing, we get

 75) 8485 (113
     75
     ---
      98
      75
      ----
       235
       225
       ---
        10
       ---
 
 Required number = (8485 - 10) // Because 10 < (75 - 10)
                 = 8475.        

65. 

If the number 42573 * is exactly divisible by 72, then the minimum value of * is:

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: Option C

Explanation:

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.


66. 

Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?

A. 639
B. 2079
C. 3791
D. 37911
E. None of these

Answer: Option B

Explanation:

639 is not divisible by 7

2079 is divisible by each of 3, 7, 9, 11.


67. 

Which natural number is nearest to 9217, which is completely divisible by 88 ?

A. 9152
B. 9240
C. 9064
D. 9184
E. None of these

Answer: Option B

Explanation:

On dividing we get, 

 88) 9217 (104
     88
     ----
      417
      352
      ----
       65
      ----
  
 Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.
                            = 9217 + 23
                            = 9240.      

68. 

(4300731) - ? = 2535618

A. 1865113
B. 1775123
C. 1765113
D. 1675123
E. None of these

Answer: Option C

Explanation:

Let 4300731 - x = 2535618

Then x, = 4300731 - 2535618 = 1765113


69. 

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?

A. 3
B. 2
C. 1
D. 0

Answer: Option B

Explanation:

Let n = 4q + 3. Then 2n = 8q + 6   = 4(2q + 1 ) + 2.

Thus, when 2n is divided by 4, the remainder is 2.


70. 

(489 + 375)2 - (489 - 375)2 = ?
(489 x 375)

A. 144
B. 864
C. 2
D. 4
E. None of these

Answer: Option D

Explanation:

Given Exp. = (a + b)2 - (a - b)2 = 4ab = 4
ab ab