# Aptitude - Numbers

- Numbers - Formulas
- Numbers - General Questions

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}

= (25*k*^{2} + 30*k* + 9)

= 5(5*k*^{2} + 6*k* + 1) + 4

On dividing *x*^{2} by 5, we get 4 as remainder.

3-digit 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.

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.

2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

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.

(963 + 476)^{2} + (963 - 476)^{2} |
= ? |

(963 x 963 + 476 x 476) |

Given Exp. = | (a + b)^{2} + (a - b)^{2} |
= | 2(a^{2} + b^{2}) |
= 2 |

(a^{2} + b^{2}) |
(a^{2} + b^{2}) |