UPSC Prelims 2010 · General Studies
Question 71: Basic Numeracy
How many numbers from 0 to 999 are not divisible by either 5 or 7 ?
AnswerThe answer is (c).
Count the whole numbers 0 to 999, which is 1,000 numbers. Divisible by 5: 200 (0, 5, ..., 995). Divisible by 7: 143 (0, 7, ..., 994). Divisible by both, that is by 35: 29 (0, 35, ..., 980). Divisible by 5 or 7: 200 + 143 - 29 = 314. Divisible by neither: 1000 - 314 = 686. Remember: use inclusion and exclusion, and do not forget 0, which is divisible by both.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 313 is how many of 1 to 999 are divisible by 5 or 7, not the number that are not.
- (b) 341 has no basis in the count.
- (c) Right: 1000 - 314 = 686.
- (d) 786 has no basis in the count.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2010, General Studies, Series A. The paper on upsc.gov.in.