How many numbers are there between 100 and 300 which either begin with or end with 2 ?
- (a) 110 ✓ UPSC's answer
- (b) 111
- (c) 112
- (d) None of the above
Why the answer is (a)
• Numbers between 100 and 300 are 101 to 299.
• Beginning with 2: 200 to 299 — 100 numbers.
• Ending with 2: 102, 112, …, 192 and 202, 212, …, 292 — 20 numbers.
• Both beginning and ending with 2: 202, 212, …, 292 — 10 numbers, counted twice above.
• Total = 100 + 20 – 10 = 110.
• Hence 110, option (a).
Why the other options are wrong
- (b) 111
- Option (b) 111 is incorrect because it likely results from an error in counting the overlap or the total set, such as including 100 or 300 incorrectly or miscounting the intersection.
- (c) 112
- Option (c) 112 is incorrect because it overcounts the valid numbers, possibly by failing to subtract the intersection of numbers starting and ending with 2 correctly.
- (d) None of the above
- Option (d) is incorrect because the calculated count of 110 matches option (a), so 'None of the above' is not applicable.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.