UPSC Prelims 2017 · CSAT
Question 79: Basic Numeracy
There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?
AnswerUPSC’s answer is (d).
Let the number be 10a + b; its reverse is 10b + a. The difference is 9(a - b) = 27, so a - b = 3. The numbers 41, 52, 63, 74, 85 and 96 qualify, and 30 too if its reverse, 03, is allowed: six or seven numbers, which is more than 5. So none of the options 3, 4 or 5 is right.
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) There are at least six such numbers, not three.
- (b) Four undercounts.
- (c) Five undercounts; at least six qualify.
- (d) Correct: the count is 6 (or 7 with 30).
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.