GATE CS 2024 Set 1 Q.2: Quantitative Aptitude

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

depends on $xy$

depends only on $x$ and not on $y$

depends only on $y$ and not on $x$

is a constant

Official answer and solution

Solution

Express the proportionality as an equation $x + y = k(x - y)$ with constant $k$ and solve for $x/y$ .

Since $(x + y)$ is proportional to $(x - y)$ , there exists a non-zero proportionality constant $k$ such that:

x + y = k(x - y)

Since $x$ and $y$ are distinct ( $x \neq y$ ) and non-zero ( $y \neq 0$ ), dividing both sides by $y$ gives:

\frac{x}{y} + 1 = k\left(\frac{x}{y} - 1\right) \implies \frac{x}{y}(k - 1) = k + 1 \implies \frac{x}{y} = \frac{k + 1}{k - 1}

Because $k$ is a constant (and $k \neq 1$ as $y \neq 0$ ), the ratio $\frac{x}{y}$ is a constant.

Final answer

Option (D)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

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