A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two-digit number. How many coins does A have in the beginning?
- (a) 76
- (b) 68
- (c) 60
- (d) 52 ✓ UPSC's answer
Why the answer is (d)
• The smallest two-digit number is 10, so D has 10 coins.
• D received half of C's coins plus 2, so C had (10 - 2) * 2 = 16 coins.
• C received half of B's coins plus 2, so B had (16 - 2) * 2 = 28 coins.
• B received half of A's coins plus 2, so A had (28 - 2) * 2 = 52 coins.
• Therefore, A started with 52 coins, which corresponds to option (d).
Why the other options are wrong
- (a) 76
- 76 is incorrect because working backwards from D's 10 coins yields 52, not 76.
- (b) 68
- 68 is incorrect because the reverse calculation of the coin distribution results in 52.
- (c) 60
- 60 is incorrect because the step-by-step deduction from D to A confirms the initial count is 52.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.