Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
61.  When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? 

Answer: Option B Explanation: x = 13p + 11 and x = 17q + 9 13p + 11 = 17q + 9 17q  13p = 2
x = (13 x 26 + 11) = (338 + 11) = 349 
62.  (51 + 52 + 53 + ... + 100) = ? 

Answer: Option D Explanation: S_{n} = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100)  (1 + 2 + 3 + ... + 50)
= (50 x 101)  (25 x 51) = (5050  1275) = 3775. 
63.  (800 ÷ 64) x (1296 ÷36) = ? 

Answer: Option E Explanation:

64.  Which natural number is nearest to 8485, which is completely divisible by 75 ? 

Answer: Option A Explanation: On dividing, we get 75) 8485 (113 75  98 75  235 225  10  Required number = (8485  10) // Because 10 < (75  10) = 8475. 
65.  If the number 42573 * is exactly divisible by 72, then the minimum value of * is: 

Answer: Option C Explanation: 72 = 9 x8, where 9 and 8 are coprime. The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6. Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9. Required value of * is 6. 
66.  Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ? 

Answer: Option B Explanation: 639 is not divisible by 7 2079 is divisible by each of 3, 7, 9, 11. 
67.  Which natural number is nearest to 9217, which is completely divisible by 88 ? 

Answer: Option B Explanation: On dividing we get, 88) 9217 (104 88  417 352  65  Therefore, Required number = 9217 + (88  65) // Because (88  65) < 65. = 9217 + 23 = 9240. 
68.  (4300731)  ? = 2535618 

Answer: Option C Explanation: Let 4300731  x = 2535618 Then x, = 4300731  2535618 = 1765113 
69.  n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ? 

Answer: Option B Explanation: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2. Thus, when 2n is divided by 4, the remainder is 2. 
70. 


Answer: Option D Explanation:
