Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
51.  476 ** 0 is divisible by both 3 and 11. The nonzero digits in the hundred's and ten's places are respectively: 

Answer: Option C Explanation: Let the given number be 476 xy 0. Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3. And, (0 + x + 7)  (y + 6 + 4) = (x  y 3) must be either 0 or 11. x  y  3 = 0 y = x  3 (17 + x + y) = (17 + x + x  3) = (2x + 14) x= 2 or x = 8. x = 8 and y = 5. 
52.  If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be: 

Answer: Option A Explanation: Given number = 97215x6 (6 + 5 + 2 + 9)  (x + 1 + 7) = (14  x), which must be divisible by 11. x = 3 
53.  (11^{2} + 12^{2} + 13^{2} + ... + 20^{2}) = ? 

Answer: Option B Explanation: (11^{2} + 12^{2} + 13^{2} + ... + 20^{2}) = (1^{2} + 2^{2} + 3^{2} + ... + 20^{2})  (1^{2} + 2^{2} + 3^{2} + ... + 10^{2})
= (2870  385) = 2485. 
54.  If the number 5 * 2 is divisible by 6, then * = ? 

Answer: Option A Explanation: 6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x. Then, (5 + x + 2) must be divisible by 3. So, x = 2. 
55.  Which of the following numbers will completely divide (49^{15}  1) ? 

Answer: Option A Explanation: (x^{n}  1) will be divisibly by (x + 1) only when n is even. (49^{15}  1) = {(7^{2})^{15}  1} = (7^{30}  1), which is divisible by (7 +1), i.e., 8. 
56. 


Answer: Option D Explanation:

57. 


Answer: Option B Explanation:

58.  On dividing 2272 as well as 875 by 3digit number N, we get the same remainder. The sum of the digits of N is: 

Answer: Option A Explanation: Clearly, (2272  875) = 1397, is exactly divisible by N. Now, 1397 = 11 x 127 The required 3digit number is 127, the sum of whose digits is 10. 
59.  A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be: 

Answer: Option C Explanation: 987 = 3 x 7 x 47 So, the required number must be divisible by each one of 3, 7, 47 553681 (Sum of digits = 28, not divisible by 3) 555181 (Sum of digits = 25, not divisible by 3) 555681 is divisible by 3, 7, 47. 
60.  How many prime numbers are less than 50 ? 

Answer: Option B Explanation: Prime numbers less than 50 are: Their number is 15 