How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place?
- (a) 64
- (b) 80
- (c) 90 ✓ UPSC's answer
- (d) 104
Why the answer is (c)
• The numbers must be strictly between 99 and 1000, meaning they range from 100 to 999.
• These are all three-digit numbers of the form XYZ, where X is the hundreds digit, Y is the tens digit, and Z is the units digit.
• The condition states that the digit 8 occupies the units place, so Z is fixed as 8.
• The hundreds digit X can be any digit from 1 to 9 (since the number must be at least 100), giving 9 possible choices.
• The tens digit Y can be any digit from 0 to 9, giving 10 possible choices.
• The total count is the product of the choices: 9 (for X) × 10 (for Y) × 1 (for Z) = 90.
Why the other options are wrong
- (a) 64
- 64 is incorrect because it does not account for the 9 possible hundreds digits and 10 possible tens digits.
- (b) 80
- 80 is incorrect because it likely assumes the hundreds digit can be 0, which would exclude valid three-digit numbers or miscount the range.
- (d) 104
- 104 is incorrect because it exceeds the maximum possible count of 90 for three-digit numbers ending in 8.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.