Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
41.  On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ? 

Answer: Option C Explanation: Let x be the number and y be the quotient. Then, x = 357 x y + 39 = (17 x 21 x y) + (17 x 2) + 5 = 17 x (21y + 2) + 5) Required remainder = 5. 
42.  If the product 4864 x 9 P 2 is divisible by 12, then the value of P is: 

Answer: Option E Explanation: Clearly, 4864 is divisible by 4. So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3. P = 1. 
43.  Which one of the following is the common factor of (47^{43} + 43^{43}) and (47^{47} + 43^{47}) ? 

Answer: Option B Explanation: When n is odd, (x^{n} + a^{n}) is always divisible by (x + a). Each one of (47^{43} + 43^{43}) and (47^{47} + 43^{47}) is divisible by (47 + 43). 
44.  84 x 29 + 365 = ? 

Answer: Option D Explanation:

45.  A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be: 

Answer: Option A Explanation: Let x = 296q + 75 = (37 x 8q + 37 x 2) + 1 = 37 (8q + 2) + 1 Thus, when the number is divided by 37, the remainder is 1. 
46.  In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been 

Answer: Option D Explanation: 5  x z = 13 x 1 + 12 = 25  9  y  4 y = 9 x z + 8 = 9 x 25 + 8 = 233  13 z  8 x = 5 x y + 4 = 5 x 233 + 4 = 1169   1 12 585) 1169 (1 585  584  Therefore, on dividing the number by 585, remainder = 584. 
47.  In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ? 

Answer: Option D Explanation: Divisor = (5 x 46) = 230
Dividend = (Divisor x Quotient) + Remainder = (230 x 23) + 46 = 5290 + 46 = 5336. 
48.  4500 x ? = 3375 

Answer: Option B Explanation:

49.  What smallest number should be added to 4456 so that the sum is completely divisible by 6 ? 

Answer: Option C Explanation: 6) 4456 (742 42  25 24 Therefore, Required number = (6  4) = 2.  16 12  4 
50.  What least number must be subtracted from 13601, so that the remainder is divisible by 87 ? 

Answer: Option C Explanation: 87) 13601 (156 87  490 435  551 522  29  Therefore, the required number = 29. 