Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
1.  Which one of the following is not a prime number? 

Answer: Option D Explanation: 91 is divisible by 7. So, it is not a prime number.

2.  (112 x 5^{4}) = ? 

Answer: Option B Explanation:

3.  It is being given that (2^{32} + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number? 

Answer: Option D Explanation: Let 2^{32} = x. Then, (2^{32} + 1) = (x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (2^{96} + 1) = [(2^{32})^{3} + 1] = (x^{3} + 1) = (x + 1)(x^{2}  x + 1), which is completely divisible by N, since (x + 1) is divisible by N. 
4.  What least number must be added to 1056, so that the sum is completely divisible by 23 ? 

Answer: Option A Explanation: 23) 1056 (45 92  136 115  21  Required number = (23  21) = 2. 
5.  1397 x 1397 = ? 

Answer: Option A Explanation:

6.  How many of the following numbers are divisible by 132 ? 

Answer: Option A Explanation: 132 = 4 x 3 x 11 So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also. 264 11,3,4 (/) 396 11,3,4 (/) 462 11,3 (X) 792 11,3,4 (/) 968 11,4 (X) 2178 11,3 (X) 5184 3,4 (X) 6336 11,3,4 (/) Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. 
7.  (935421 x 625) = ? 

Answer: Option B Explanation:
= 584638125 
8.  The largest 4 digit number exactly divisible by 88 is: 

Answer: Option A Explanation: Largest 4digit number = 9999 88) 9999 (113 88  119 88  319 264  55  Required number = (9999  55) = 9944. 
9.  Which of the following is a prime number ? 

Answer: Option D Explanation:
Clearly, 97 is a prime number.

10.  What is the unit digit in {(6374)^{1793} x (625)^{317} x (341^{491})}? 

Answer: Option A Explanation: Unit digit in (6374)^{1793} = Unit digit in (4)^{1793} = Unit digit in [(4^{2})^{896} x 4] = Unit digit in (6 x 4) = 4 Unit digit in (625)^{317} = Unit digit in (5)^{317} = 5 Unit digit in (341)^{491} = Unit digit in (1)^{491} = 1 Required digit = Unit digit in (4 x 5 x 1) = 0. 