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GATE 2018 ME (ME1) – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Integers a and b satisfy that $a+a^2b^3$ is odd. Which is correct?

  1. a and b are both odd
  2. a and b are both even
  3. a is even and b is odd
  4. a is odd and b is even

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Show answer and explanation

Correct answer: (D) a is odd and b is even

Explanation

If a were even, both terms would be even, so a must be odd. Then $a^2$ is odd, and the total is odd only if $b^3$ is even. Thus b is even (D).