UPSC Prelims 2023 · CSAT
Question 4: Basic Numeracy
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make ?
AnswerUPSC’s answer is (d).
A pair of shoes needs one left and one right shoe. Total shoes: red 20 (10 left, 10 right), white 18, black 16. Worst case: he first draws all 18 white and 16 black shoes (34), then all 10 red shoes of one foot (10). That is 44 attempts and still no red pair. The 45th shoe must be the other foot in red, completing a pair. Maximum attempts = 34 + 10 + 1 = 45.
Why each option is right or wrong
- (a) Wrong: 27 is the number of pairs (10 + 9 + 8), not shoes drawn.
- (b) Wrong: 36 = 34 + 2 treats any two red shoes as a pair, ignoring left and right.
- (c) Wrong: 44 draws can still fail; the 45th is needed.
- (d) Right: 34 other shoes + 10 red of one foot + 1 more = 45.
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.