Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
31.  On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ? 

Answer: Option D Explanation: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder. x = 5k + 3 x^{2} = (5k + 3)^{2} = (25k^{2} + 30k + 9) = 5(5k^{2} + 6k + 1) + 4 On dividing x^{2} by 5, we get 4 as remainder. 
32.  How many 3digit numbers are completely divisible 6 ? 

Answer: Option B Explanation: 3digit number divisible by 6 are: 102, 108, 114,... , 996 This is an A.P. in which a = 102, d = 6 and l = 996 Let the number of terms be n. Then t_{n} = 996. a + (n  1)d = 996 102 + (n  1) x 6 = 996 6 x (n  1) = 894 (n  1) = 149 n = 150 Number of terms = 150. 
33.  How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ? 

Answer: Option D Explanation: Required numbers are 24, 30, 36, 42, ..., 96 This is an A.P. in which a = 24, d = 6 and l = 96 Let the number of terms in it be n. Then t_{n} = 96 a + (n  1)d = 96 24 + (n  1) x 6 = 96 (n  1) x 6 = 72 (n  1) = 12 n = 13 Required number of numbers = 13. 
34.  How many of the following numbers are divisible by 3 but not by 9 ? 

Answer: Option B Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 9 (X) 2343 12 (/) 3474 18 (X) 4131 9 (X) 5286 21 (/) 5340 12 (/) 6336 18 (X) 7347 21 (/) 8115 15 (/) 9276 24 (/) Required number of numbers = 6. 
35. 


Answer: Option C Explanation:

36.  How many 3 digit numbers are divisible by 6 in all ? 

Answer: Option B Explanation: Required numbers are 102, 108, 114, ... , 996 This is an A.P. in which a = 102, d = 6 and l = 996 Let the number of terms be n. Then, a + (n  1)d = 996 102 + (n  1) x 6 = 996 6 x (n  1) = 894 (n  1) = 149 n = 150. 
37.  A 3digit number 4a3 is added to another 3digit number 984 to give a 4digit number 13b7, which is divisible by 11. Then, (a + b) = ? 

Answer: Option A Explanation: 4 a 3  9 8 4 } ==> a + 8 = b ==> b  a = 8 13 b 7  Also, 13 b7 is divisible by 11 (7 + 3)  (b + 1) = (9  b) (9  b) = 0 b = 9 (b = 9 and a = 1) (a + b) = 10. 
38.  8597  ? = 7429  4358 

Answer: Option C Explanation: 7429 Let 8597  x = 3071 4358 Then, x = 8597  3071  = 5526 3071  
39.  The smallest prime number is: 

Answer: Option B Explanation:
The smallest prime number is 2.

40.  (12345679 x 72) = ? 

Answer: Option B Explanation:
