UPSC Prelims 2006 · General Studies
Question 62: Basic Numeracy
A box contains 5 sets of balls while there are 3 balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed?
AnswerThe answer is (a).
There are 5 colours, so by the pigeonhole principle, picking 5 balls could give one of each colour with no pair, and the sixth ball must repeat a colour. So at least 6 balls must be removed to be certain of having a pair of the same colour. The fact that each colour has 3 balls only ensures a pair is always possible.
Why each option is right or wrong
- (a) Correct: 5 colours, so the sixth ball guarantees a matching pair.
- (b) 7 would be more than needed.
- (c) 8 would be more than needed.
- (d) 9 would be more than needed.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.