The GATE Grind

GATE 2018 EE – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

For what values of $k$ given below is $\dfrac{(k+2)^2}{k-3}$ an integer?

  1. 4, 8, 18
  2. 4, 10, 16
  3. 4, 8, 28
  4. 8, 26, 28

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 4, 8, 28

Explanation

Write $(k+2)^2=(k-3)(k+7)+25$, so the expression is an integer only when $(k-3)$ divides 25. So $k-3\in\{1,5,25\}$, i.e. $k=4,8,28$.