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GATE 2024 CS (CS1) – Question 2

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

If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\frac{x}{y}$

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

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Show answer and explanation

Correct answer: (D) is a constant

Explanation

$x+y=k(x-y)$ gives $x(1-k)=-y(1+k)$, so $x/y=-(1+k)/(1-k)$, which is a constant depending only on $k$.