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GATE 2017 CS – Question 8

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

The expression $\dfrac{(x + y) - |x - y|}{2}$ is equal to

  1. the maximum of $x$ and $y$
  2. the minimum of $x$ and $y$
  3. 1
  4. none of the above

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Correct answer: (B) the minimum of $x$ and $y$

Explanation

If $x \geq y$ then $|x - y| = x - y$ and the expression is $\frac{x + y - x + y}{2} = y$, the smaller value. If $x < y$ it is $\frac{x + y - y + x}{2} = x$, which is again the smaller value. So it gives the minimum of $x$ and $y$.