How many of the following numbers are divisible by 3 but not by

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.

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

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.

A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?

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.

8597 - ? = 7429 - 4358

7429-4358=3071

Let 8597 - x = 3071

Then, x = 8597 - 3071 = 5526

The smallest prime number is: