Finding the integral solutions of a given equation is a question type that commonly appear in CAT and similar topics. Most of these questions requires a fundamental understanding of Algebra and PnC. Some times this could get bit tricky and we will end up missing cases or wasting time to find the cases. There are many useful tricks and direct formulas in this area which comes handy during exams. In this article we have collated 60 questions from this topic which were shared in various forums. Solve them all and the concepts and tricks would be clear to you. Happy learning.

# Quant

x2 + y2 - 14x - 6y - 6 = 0 |

Two digit numbers with no digit repeated = 9C1 x 9C1 = 81 |

let two numbers x and y and their lcm is 22 * 33 * 53 |

Example : |

Cyclicity of 3 : 3^1 =3; 3^2 = 9; 3^3 = 27 ; 3^4 = 81 ; 3^5= 243 . Hence again, after 4 terms starting from 1, the unit digit of powers of 3 get repeated. Hence the cycle order for 3 = 4 |

Hence, with these factors if we multiply the 2 we took out, we will get the total even factors. |

First we will understand some basic stuffs: Let say you have 10 mango of same kind, 20 banana of same kind and 30 apple of same kind. Now you have options to select none or 1 or more than 1 items (any number of items) |

Now there are 4 ways to choose a, 4 ways for b and 4 ways for c => There are 4 *4 * 4 = 64 three-digit numbers that can be made using 1,2,3 and / or 4. |