UPSC Prelims 2026 · CSAT
Question 23: Basic Numeracy
There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?
AnswerUPSC’s answer is (b).
Let k be the number of 1 kg weights (8 to 11) and make the other 20 − k kg from 2, 5 and 10 kg weights. k = 8: 12 kg is six 2s, or one 2 and a 10, or one 2 and two 5s: 3 ways. k = 9: 11 kg is one 5 and three 2s: 1 way. k = 10: 10 kg is five 2s, a single 10, or two 5s: 3 ways. k = 11: 9 kg is one 5 and two 2s: 1 way. Total 3 + 1 + 3 + 1 = 8.
Why each option is right or wrong
- (a) Wrong: 7 misses one valid combination.
- (b) Right: 3 + 1 + 3 + 1 = 8.
- (c) Wrong: 9 overcounts.
- (d) Wrong: 10 overcounts.
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.