If two distinct non-zero real variables x and y are such that (x + y) is proportional to (x - y) then the value of xy A) depends on xy B) depends only on x and not on y C) depends only on y and not on x D) is a constant

Official answer: D) is a constant. Explanation: Given that (x + y) is directly proportional to (x - y): (x + y) = k(x - y) where k is a non-zero proportionality constant (k 1, since y 0). Rearranging the terms: x + y = kx - ky y + ky = kx - x y(1 + k) = x(k - 1) Dividing both sides by y(k - 1) (since x and y are distinct, x - y 0 k 1): xy = 1 + kk - 1 Since k is a fixed constant, 1 + kk - 1 is also a fixed constant. Therefore, the value of xy is a constant. Hence, D is the correct option.

B) depends only on x and not on y

C) depends only on y and not on x

General Aptitude · Quantitative Aptitude

Official IIT answer key · IISc Bangalore · Audited Aug 2026

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GATE CSE 2024 Set 1 Q2 · MCQ · 1 mark

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

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Quantitative Aptitude in GATE CS evaluates foundational mathematical reasoning, arithmetic, algebra, combinatorics, elementary probability, and geometry through concise word problems and functional/graphical models. The questions emphasize direct application of core algebraic identities, logarithmic laws, rates, proportions, set intersections, and calculus-based optimization rather than heavy computation. Items are evenly distributed between 1-mark conceptual or single-step problems and 2-mark multi-step arithmetic, geometric, or conditional reasoning setups.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

General Aptitude · Quantitative Aptitude

Official IIT answer key · IISc Bangalore · Audited Aug 2026

Take topic test

GATE CSE 2024 Set 1 Q2 · MCQ · 1 mark

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

Select an option to check

Key concept

Quantitative Aptitude

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Quantitative Aptitude

Full Quantitative Aptitude guide →

More on Quantitative Aptitude

All 53 questions on Quantitative Aptitude →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

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

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

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

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

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More from GATE CSE 2024 Set 1

More on Quantitative Aptitude

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

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