Aptitude - Numbers

Exercise :: Numbers - General Questions

21. 

Which of the following number is divisible by 24 ?

A. 35718
B. 63810
C. 537804
D. 3125736

Answer: Option D

Explanation:

24 = 3 x8, where 3 and 8 co-prime.

Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.

Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.

Consider option (D),

Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.

Also, 736 is divisible by 8.

3125736 is divisible by (3 x 8), i.e., 24.


22. 

753 x 753 + 247 x 247 - 753 x 247 = ?
753 x 753 x 753 + 247 x 247 x 247

A.
1
1000
B.
1
506
C.
253
500
D. None of these

Answer: Option A

Explanation:

Given Exp. = (a2 + b2 - ab) = 1 = 1 = 1
(a3 + b3) (a + b) (753 + 247) 1000

23. 

(?) + 3699 + 1985 - 2047 = 31111

A. 34748
B. 27474
C. 30154
D. 27574
E. None of these

Answer: Option B

Explanation:

x + 3699 + 1985 - 2047 = 31111

   x + 3699 + 1985 = 31111 + 2047

   x + 5684 = 33158

   x = 33158 - 5684 = 27474.


24. 

If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:

A. 2
B. 5
C. 6
D. 7
E. None of these

Answer: Option D

Explanation:

Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.

   x = 7.


25. 

The difference between the local value and the face value of 7 in the numeral 32675149 is

A. 75142
B. 64851
C. 5149
D. 69993
E. None of these

Answer: Option D

Explanation:

(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993

26. 

The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

A.
3
5
B.
3
10
C.
4
5
D.
4
3

Answer: Option C

Explanation:

Let the required fraction be x. Then 1 - x = 9
x 20

    1 - x2 = 9
x 20

     20 - 20x2 = 9x

     20x2 + 9x - 20 = 0

     20x2 + 25x - 16x - 20 = 0

     5x(4x + 5) - 4(4x + 5) = 0

     (4x + 5)(5x - 4) = 0

x = 4
5


27. 

On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?

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

Answer: Option B

Explanation:

Formula: (Divisor*Quotient) + Remainder = Dividend.

Soln:

(56*Q)+29 = D -------(1)

D%8 = R -------------(2)

From equation(2),

((56*Q)+29)%8 = R.

=> Assume Q = 1.

=> (56+29)%8 = R.

=> 85%8 = R

=> 5 = R.


28. 

If n is a natural number, then (6n2 + 6n) is always divisible by:

A. 6 only
B. 6 and 12 both
C. 12 only
D. by 18 only

Answer: Option B

Explanation:

(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.


29. 

107 x 107 + 93 x 93 = ?

A. 19578
B. 19418
C. 20098
D. 21908
E. None of these

Answer: Option C

Explanation:

107 x 107 + 93 x 93 = (107)2 + (93)2
= (100 + 7)2 + (100 - 7)2
= 2 x [(100)2 + 72]       [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)]
= 20098

30. 

What will be remainder when (6767 + 67) is divided by 68 ?

A. 1
B. 63
C. 66
D. 67

Answer: Option C

Explanation:

(xn + 1) will be divisible by (x + 1) only when n is odd.

(6767 + 1) will be divisible by (67 + 1)

(6767 + 1) + 66, when divided by 68 will give 66 as remainder.