Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
21.  Which of the following number is divisible by 24 ? 

Answer: Option D Explanation: 24 = 3 x8, where 3 and 8 coprime. 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. 


Answer: Option A Explanation:

23.  (?) + 3699 + 1985  2047 = 31111 

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: 

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 

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: 

Answer: Option C Explanation:
20  20x^{2} = 9x 20x^{2} + 9x  20 = 0 20x^{2} + 25x  16x  20 = 0 5x(4x + 5)  4(4x + 5) = 0 (4x + 5)(5x  4) = 0

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

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 (6n^{2} + 6n) is always divisible by: 

Answer: Option B Explanation: (6n^{2} + 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 = ? 

Answer: Option C Explanation:

30.  What will be remainder when (67^{67} + 67) is divided by 68 ? 

Answer: Option C Explanation: (x^{n} + 1) will be divisible by (x + 1) only when n is odd. (67^{67} + 1) will be divisible by (67 + 1) (67^{67} + 1) + 66, when divided by 68 will give 66 as remainder. 