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GATE 2024 MT – Question 2

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

Two distinct nonzero real variables $x,y$ satisfy $(x+y)\propto(x-y)$. The value of $x/y$

  1. depends on $xy$
  2. depends only on $x$, not on $y$
  3. depends only on $y$, not on $x$
  4. is a constant

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Show answer and explanation

Correct answer: (D) is a constant

Explanation

Write x+y=k(x−y), with constant k.

Rearranging gives (k−1)x=(k+1)y, hence x/y=(k+1)/(k−1).

Since the variables are nonzero, k=1 is excluded.

The ratio is a **constant, D**.