2023 CSAT, all questions
UPSC Prelims 2023 · CSAT
Question 48: Basic Numeracy
What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction ?
a3
b11
c12
d66
AnswerUPSC’s answer is (c).
In a circle of 12, a run of 10 consecutive things in the clockwise direction is fixed by where it starts. There are 12 possible starting points and each gives a different selection. Equivalently, the 2 things left out must be neighbours, and a circle of 12 has 12 adjacent pairs. So there are 12 selections.
Why each option is right or wrong
- (a) Wrong: 3 would be the count for a straight line of 12, not a circle.
- (b) Wrong: a circle has 12 starting points, not 11.
- (c) Right: 12 starting points give 12 selections.
- (d) Wrong: 66 counts any two left-out items, not only adjacent ones.
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.