UPSC Prelims 2026 · CSAT
Question 30: Basic Numeracy
Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x^2 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?
AnswerUPSC’s answer is (b).
y is proportional to x², and x is inversely proportional to z, so y is proportional to 1/z²: y × z² is constant. From z = 7/25 and y = 50 the constant is 50 × 49/625 = 98/25. For y = 98, z² = (98/25)/98 = 1/25, so z = 1/5.
Why each option is right or wrong
- (a) Wrong: z = 1/7 gives y z² = 2, not 98/25.
- (b) Right: 98 × (1/25) = 98/25.
- (c) Wrong: z = 5/7 gives y z² = 50, not 98/25.
- (d) Wrong: z = 1 gives y z² = 98.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.