UPSC Prelims 2006 · General Studies
Question 136: Basic Numeracy
How many numbers are there in all 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?
AnswerThe answer is (c).
There are 1,000 numbers from 6000 to 6999. Count those with no repeated digit: the first digit is 6, and the other three come from the nine remaining digits, all different: 9 x 8 x 7 = 504. So numbers with at least one repeated digit = 1000 - 504 = 496.
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) 216 does not match the count.
- (b) 356 does not match the count.
- (c) Correct: 1000 - 504 = 496.
- (d) 504 is the count of numbers with no repeated digit.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.