Distinct nonzero real variables x, y satisfy (x+y)(x-y). What can be said about x/y?

GATE 2024 AG – Question 2

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

Distinct nonzero real variables x, y satisfy $(x+y)\propto(x-y)$. What can be said about x/y?

Depends on xy
Depends only on x
Depends only on y
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 fixed proportionality constant k. Rearranging gives $(k-1)x=(k+1)y$,so $x/y=(k+1)/(k-1)$ is constant. Nonzero y excludes k=1 for a valid pair. Therefore **D**.

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