# Aptitude - Numbers

### Exercise :: Numbers - General Questions

21.

Which of the following number is divisible by 24 ?

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

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

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

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

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

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

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

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

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

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

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.