UPSC Prelims 2007 Q146: Science & Technology – Quantitative Aptitude
If all the numbers from 501 to 700 are written, what is the total number of times the digit 6
appears?
- (a) 138
- (b) 139
- (c) 140
- (d) 141
Answer: (c) 140
Explanation
How many times does digit 6 appear from 501 to 700?
Count each place separately.
| Place | Numbers | Count |
|---|---|---|
| Hundreds | 600 to 699 | 100 |
| Tens | 560-569 and 660-669 | 10 + 10 = 20 |
| Units | 506, 516 … 596 and 606, 616 … 696 | 10 + 10 = 20 |
| Total | 100 + 20 + 20 | 140 |
(700 has no 6, and 501-599 has no 6 in the hundreds place.)
Answer: (c) 140.
Why each option is right or wrong
- (a) Incorrect. 138 misses two occurrences.
- (b) Incorrect. 139 misses one occurrence — often 666 counted once instead of three times.
- (c) CORRECT. 100 (hundreds) + 20 (tens) + 20 (units) = 140.
- (d) Incorrect. 141 over-counts; the place-by-place total is 140.
Key point
Count digit 6 by place: hundreds 100 + tens 20 + units 20 = 140.
Remember
Digit 6 appears 140 times from 501 to 700.
Common mistakes
- Counting numbers that contain 6 instead of times 6 appears — 666 counts three times.
- Forgetting the tens-place 6s in the 500s (560-569).
- Including 500 or leaving out 700 wrongly — neither has a 6, so the range ends do not matter here.
Exam tip
'How many times does a digit appear' → count place by place. Never list all numbers.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Numbers)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Number System)