52.  If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:  

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. 



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 