GATE 2020 CY – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

An engineer measures X,Y,Z and finds the plotted straight-line relationship through the origin between product XY and Z. Which statement is FALSE?

For fixed Z, X is proportional to Y.
For fixed Y, X is proportional to Z.
For fixed X, Z is proportional to Y.
XY/Z is constant.

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Show answer and explanation

Correct answer: (A) For fixed Z, X is proportional to Y.

Explanation

The graph means XY = kZ. With fixed Z, $X=kZ/Y$, so X is inversely proportional to Y, not directly proportional. Thus A is false. Fixing Y gives X ∝ Z, fixing X gives Z ∝ Y, and XY/Z = k where defined.

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