Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
- (a) 1/7
- (b) 1/5 ✓ UPSC's answer
- (c) 5/7
- (d) 1
Why the answer is (b)
• y ∝ x² and x ∝ 1/z, so y ∝ 1/z², i.e. y × z² is constant.
• At the given point: 50 × (7/25)².
• For y = 98: z² = 50 × (7/25)² ÷ 98 = (7/25)² × (25/49), so z = (7/25) × (5/7) = 1/5: (b).
Why the other options are wrong
- (a) 1/7
- 1/7 does not satisfy y × z² = constant.
- (c) 5/7
- 5/7 would make y smaller than 50, not 98.
- (d) 1
- z = 1 would make y much smaller, not 98.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.