UPSC Prelims 2017 · CSAT
Question 56: Basic Numeracy
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?
AnswerUPSC’s answer is (b).
To be sure of at least one ball of every colour, consider the worst case: you pick all the balls of the two most plentiful colours first. That is 8 green + 7 white = 15 balls with no red. The very next ball must be red, so 15 + 1 = 16 picks guarantee all three colours. Always add one to the worst-case total of the two largest groups.
Why each option is right or wrong
- (a) 17 would work but is not the minimum: 16 already guarantees all three colours.
- (b) Correct: worst case 8 + 7 = 15 balls, then 1 more.
- (c) 13 balls can be 8 green and 5 red with no white.
- (d) 11 balls can miss a colour, for example 8 green and 3 red.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.