An engineer measures THREE quantities, X, Y, and Z in an experiment. She finds that they follow a relationship that is represented in the figure below (the product of X and Y linearly varies with Z). Then, which of the following statements is FALSE? A. For fixed Z, X is proportional to Y B. For fixed X, Z is proportional to Y C. XY / Z = constant D. XY : Z = constant

GATE 2020 · General Aptitude · Ratio Proportion · medium

Answer: Statement A is FALSE. For fixed Z, X and Y are inversely proportional (their product is constant), not directly proportional. Answer: A.

1. Identify the mathematical relationship: The graph shows XY linearly varies with Z passing through origin, so XY = kZ, equivalently XY/Z = k = constant.
2. Test statement A: For fixed Z, X is proportional to Y: With Z fixed, XY = constant, so X = C/Y. This means X is INVERSELY proportional to Y, not directly proportional. Statement A is FALSE.
3. Verify other statements are TRUE: B is true (Y proportional to Z when X fixed). C and D both state XY/Z = constant, which directly follows from XY = kZ.