A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is
- (a) 1
- (b) 2 ✓ UPSC's answer
- (c) 3
- (d) 4
Why the answer is (b)
• Let the number be a0c. Its digits add to 4, so a + c = 4.
• Interchanging the first and last digits gives c0a, and c0a – a0c = 99(c – a) = 198, so c – a = 2.
• So the first and last digits differ by 2 (the number is 103 and the new number 301), option (b).
Why the other options are wrong
- (a) 1
- A difference of 1 would make the gap 99, not 198.
- (c) 3
- A difference of 3 would make the gap 297, not 198.
- (d) 4
- A difference of 4 would make the gap 396, not 198.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.