How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?
- (a) 5
- (b) 11
- (c) 12 ✓ UPSC's answer
- (d) 13
Why the answer is (c)
• List all integers from 1 to 100 containing the digit 4: 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94, total 19.
• Identify those divisible by 4: 4, 24, 40, 44, 48, 64, 84, total 7.
• Subtract the divisible-by-4 numbers from the total: 19 - 7 = 12.
• Therefore the official key option (c) 12 follows.
Why the other options are wrong
- (a) 5
- Option (a) 5 is wrong because 19 numbers contain the digit 4 and only 7 of them are divisible by 4, leaving 12, not 5.
- (b) 11
- Option (b) 11 is wrong because the correct count of numbers containing 4 and not divisible by 4 is 12, not 11.
- (d) 13
- Option (d) 13 is wrong because subtracting the 7 divisible-by-4 numbers from the 19 numbers containing 4 gives 12, not 13.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.