UPSC Prelims 2024 · CSAT
Question 20: Basic Numeracy
Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10 :
- 1.The unit digit of S can be 0.
- 2.The unit digit of S can be 9.
- 3.The unit digit of S can be 5.
Which of the statements given above are correct?
AnswerUPSC’s answer is (c).
The primes below 10 are 2, 3, 5 and 7; choosing three distinct ones gives the sums 2 + 3 + 5 = 10, 2 + 3 + 7 = 12, 2 + 5 + 7 = 14 and 3 + 5 + 7 = 15. The unit digits are 0, 2, 4 and 5. So a unit digit of 0 (statement 1) and of 5 (statement 3) are possible, while 9 (statement 2) never appears. Remember to list all the cases when the set is small.
- 1. 2 + 3 + 5 = 10 ends in 0.
- 2. No sum ends in 9; the four sums are 10, 12, 14 and 15.
- 3. 3 + 5 + 7 = 15 ends in 5.
How you could have got this
- If you were sure statement 2 is not correct, (a), (b) and (d) go: each of them includes 2.
What you needed to know: No sum ends in 9; the four sums are 10, 12, 14 and 15.
Only (c) is left. You didn’t need statements 1 or 3.
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) Wrong. It includes statement 2, but no sum ends in 9.
- (b) Wrong. It includes statement 2 and leaves out statement 1.
- (c) Right. 10 and 15 are possible sums, ending in 0 and 5.
- (d) Wrong. Statement 2 is not possible.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.