UPSC Prelims 2017 · CSAT
Question 49: Basic Numeracy
Certain 3-digit numbers have the following characteristics :
- 1.All the three digits are different.
- 2.The number is divisible by 7.
- 3.The number on reversing the digits is also divisible by 7.
How many such 3-digit numbers are there?
AnswerUPSC’s answer is (b).
If abc and cba are both divisible by 7, their difference 99(a - c) is too; 99 has no factor 7, so a - c is a multiple of 7. Digits differ, so |a - c| = 7, giving (a, c) = (8,1), (9,2), (1,8), (2,9); the pairs (7,0) and (0,7) fail because the middle digit would have to repeat a digit, or the number would start with zero. Testing the middle digit: 861 and 168 (middle 6), 952 and 259 (middle 5). So there are 4 numbers.
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) More than 2 qualify: 861, 168, 952 and 259 all work.
- (b) Correct: 861, 168, 952 and 259.
- (c) Only four numbers pass; no other digit pair works.
- (d) Eight would need more digit pairs than the gap-of-7 rule allows.
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.