# Aptitude - Problems on Numbers

- Problems on Numbers - Formulas
- Problems on Numbers - General Questions
- Problems on Numbers - Data Sufficiency 1
- Problems on Numbers - Data Sufficiency 2

Let the numbers be *x* and *y*.

Then, xy = 9375 and |
x |
= 15. |

y |

xy |
= | 9375 |

(x/y) |
15 |

*y*^{2} = 625.

*y* = 25.

*x* = 15*y* = (15 x 25) = 375.

Sum of the numbers = *x* + *y* = 375 + 25 = 400.

Let the numbers be *x* and *y*.

Then, *x**y* = 120 and *x*^{2} + *y*^{2} = 289.

(*x* + *y*)^{2} = *x*^{2} + *y*^{2} + 2*x**y* = 289 + (2 x 120) = 529

*x* + *y* = 529 = 23.

Let the middle digit be *x*.

Then, 2*x* = 10 or *x* = 5. So, the number is either 253 or 352.

Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.

Hence, required number = 253.

Let the numbers be *x* and *y*.

Then, *x* + *y* = 25 and *x* - *y* = 13.

4*x**y* = (*x* + *y*)^{2} - (*x*- *y*)^{2}

= (25)^{2} - (13)^{2}

= (625 - 169)

= 456

*x**y* = 114.

Let the numbers be *x* and *x* + 2.

Then, (*x* + 2)^{2} - *x*^{2} = 84

4*x* + 4 = 84

4*x* = 80

*x* = 20.

The required sum = *x* + (*x* + 2) = 2*x* + 2 = 42.