Aptitude - Numbers

Exercise :: Numbers - General Questions

51. 

476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:

A. 7 and 4
B. 7 and 5
C. 8 and 5
D. None of these

Answer: Option C

Explanation:

Let the given number be 476 xy 0.

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.

x - y - 3 = 0    y = x - 3

(17 + x + y) = (17 + x + x - 3) = (2x + 14)

x= 2 or x = 8.

x = 8 and y = 5.


52. 

If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:

A. 3
B. 2
C. 1
D. 5
E. None of these

Answer: Option A

Explanation:

Given number = 97215x6

(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.

  x = 3


53. 

(112 + 122 + 132 + ... + 202) = ?

A. 385
B. 2485
C. 2870
D. 3255

Answer: Option B

Explanation:

(112 + 122 + 132 + ... + 202) = (12 + 22 + 32 + ... + 202) - (12 + 22 + 32 + ... + 102)

Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1)    
6

20 x 21 x 41 - 10 x 11 x 21
6 6

= (2870 - 385)

= 2485.


54. 

If the number 5 * 2 is divisible by 6, then * = ?

A. 2
B. 3
C. 6
D. 7

Answer: Option A

Explanation:

6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.

Then, (5 + x + 2) must be divisible by 3. So, x = 2.


55. 

Which of the following numbers will completely divide (4915 - 1) ?

A. 8
B. 14
C. 46
D. 50

Answer: Option A

Explanation:

(xn - 1) will be divisibly by (x + 1) only when n is even.

(4915 - 1) = {(72)15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8.


56. 

9 + 3 + 7 + 2 - 9 + 1 = ?
4 17 15

A.
7 + 719
1020
B.
9 + 817
1020
C.
9 + 719
1020
D.
7 + 817
1020
E. None of these

Answer: Option D

Explanation:

Given sum
= 9 + 3 + 7 + 2 - 9 + 1
4 17 15
= (9 + 7 - 9) + 3 + 2 - 1
4 17 15
= 7 + 765 + 120 - 68
1020
= 7 + 817
1020

57. 

1 - 1 + 1 - 2 + 1 - 3 + ... up to n terms = ?
n n n

A.
1 n
2
B.
1 (n - 1)
2
C.
1 n(n - 1)
2
D. None of these

Answer: Option B

Explanation:

Given sum
= (1 + 1 + 1 + ... to n terms) - 1 + 2 + 3 + ... to n terms
n n n
= n - n 1 + 1     [ Ref: nth terms = (n/n) = 1]
2 n
= n - n + 1
2
= 1 (n - 1)
2

58. 

On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:

A. 10
B. 11
C. 12
D. 13

Answer: Option A

Explanation:

Clearly, (2272 - 875) = 1397, is exactly divisible by N.

Now, 1397 = 11 x 127

The required 3-digit number is 127, the sum of whose digits is 10.


59. 

A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:

A. 553681
B. 555181
C. 555681
D. 556581

Answer: Option C

Explanation:

987 = 3 x 7 x 47

So, the required number must be divisible by each one of 3, 7, 47

553681 (Sum of digits = 28, not divisible by 3)

555181 (Sum of digits = 25, not divisible by 3)

555681 is divisible by 3, 7, 47.


60. 

How many prime numbers are less than 50 ?

A. 16
B. 15
C. 14
D. 18

Answer: Option B

Explanation:

Prime numbers less than 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Their number is 15