UPSC Prelims 2026 · CSAT
Question 38: Basic Numeracy
In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
AnswerUPSC’s answer is (b).
Let c be the correct answers and w the wrong ones; all questions were attempted. 5c − 2w = 69 and 4c − w = 84. From the second, w = 4c − 84. Substituting: 5c − 8c + 168 = 69, so c = 33 and w = 48. Check: 165 − 96 = 69 and 132 − 48 = 84. Total questions = 33 + 48 = 81.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows UPSC’s provisional key; the final key could change it.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: 99 does not satisfy both scores.
- (b) Right: 33 + 48 = 81.
- (c) Wrong: 84 is the second score, not the question count.
- (d) Wrong: 79 does not satisfy both scores.
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.