UPSC Prelims 2023 · CSAT
Question 54: Logical Reasoning and Mental Ability
40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again ?
AnswerUPSC’s answer is (b).
The ring moves 1, 2, 3, ... places each time, so after k passes it is at child 1 + k(k + 1)/2, counted round the circle of 40. It returns to child 1 when k(k + 1)/2 is a multiple of 40. The smallest such k is 15: 15 x 16/2 = 120 = 3 x 40. For k = 1 to 14 the values 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105 are none multiples of 40. So 15.
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.
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: after 14 passes the ring is with child 26 (1 + 105 = 106, minus 80).
- (b) Right: the 15th pass returns it to child 1 (120 = 3 x 40).
- (c) Wrong: it is already back with child 1 at 15.
- (d) Wrong: it is already back with child 1 at 15.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.