# 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 ten's digit be *x* and unit's digit be *y*.

Then, *x* + *y* = 15 and *x* - *y* = 3 or *y* - *x* = 3.

Solving *x* + *y* = 15 and *x* - *y* = 3, we get: *x* = 9, *y* = 6.

Solving *x* + *y* = 15 and *y* - *x* = 3, we get: *x* = 6, *y* = 9.

So, the number is either 96 or 69.

Hence, the number cannot be determined.

Let the numbers be *a*, *b* and *c*.

Then, *a*^{2} + *b*^{2} + *c*^{2} = 138 and (*ab* + *bc* + *ca*) = 131.

(a + b + c)^{2} = *a*^{2} + *b*^{2} + *c*^{2} + 2(*ab* + *bc* + *ca*) = 138 + 2 x 131 = 400.

(*a* + *b* + *c*) = 400 = 20.

Video Explanation: https://youtu.be/qmJ-0X8j_xQ

Let the ten's digit be *x* and unit's digit be *y*.

Then, number = 10*x* + *y*.

Number obtained by interchanging the digits = 10*y* + *x*.

(10*x* + *y*) + (10*y* + *x*) = 11(*x* + *y*), which is divisible by 11.

Video Explanation: https://youtu.be/lytJE8GqRvM

Let the ten's digit be *x*.

Then, unit's digit = *x* + 2.

Number = 10*x* + (*x* + 2) = 11*x* + 2.

Sum of digits = *x* + (*x* + 2) = 2*x* + 2.

(11*x* + 2)(2*x* + 2) = 144

22*x*^{2} + 26*x* - 140 = 0

11*x*^{2} + 13*x* - 70 = 0

(*x* - 2)(11*x* + 35) = 0

*x* = 2.

Hence, required number = 11*x* + 2 = 24.

Let the number be *x*.

Then, x + 17 = |
60 |

x |

*x*^{2} + 17*x* - 60 = 0

(*x* + 20)(*x* - 3) = 0

*x* = 3.