UPSC Prelims 2020 · CSAT
Question 10: Basic Numeracy
How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?
AnswerUPSC’s answer is (a).
The digits 1 to 5 add up to 15, a multiple of 3. A number whose digit sum is a multiple of 3 is divisible by 3, so every arrangement of these five digits is divisible by 3. All of them are far larger than 3, so none can be prime. The count is zero without listing the 120 arrangements.
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.
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) Right: every arrangement is divisible by 3, so none is prime.
- (b) One would need an arrangement not divisible by 3, and none exists.
- (c) Nine primes would again need arrangements not divisible by 3.
- (d) Ten fails for the same reason.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.