UPSC Prelims 2010 · General Studies
Question 28: Basic Numeracy
A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible ?
AnswerThe answer is (d).
Each of the 10 questions can be answered in 2 ways, True or False, independently of the others. The number of different answer sequences is therefore 2 x 2 x ... (ten times) = 2^10 = 1024. Remember: n independent yes/no choices give 2^n outcomes. The options 20 and 40 come from multiplying 10 by small numbers, which does not count sequences.
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.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
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) 20 is 10 x 2, not a count of sequences.
- (b) 40 has no basis in the counting.
- (c) 512 is 2^9, which would be right for 9 questions.
- (d) Right: 2^10 = 1024.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2010, General Studies, Series A. The paper on upsc.gov.in.