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GATE 2017 ME (ME2) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

If a and b are integers and a−b is even, which must always be even?

  1. $ab$
  2. $a^2+b^2+1$
  3. $a^2+b+1$
  4. $ab-b$

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Show answer and explanation

Correct answer: (D) $ab-b$

Explanation

The condition means a and b have the same parity. Expression ab−b=b(a−1) is even: if b is even its first factor is even, while if b is odd then a is odd and a−1 is even. Thus **D** always holds. For both odd, ab is odd; the other two candidates are also odd under the stated parity condition.