UPSC Prelims 2009 · General Studies
Question 96: Basic Numeracy
How many numbers lie between 300 and 500 in which 4 comes only one time?
AnswerThe answer is (a).
Count three-digit numbers from 301 to 499 with exactly one 4. For 3__: the 4 can be the tens digit (units not 4: 9 ways) or the units digit (tens not 4: 9 ways), giving 18. For 4__: the hundreds 4 is the only 4, so tens and units avoid 4: 9 x 9 = 81. Total 18 + 81 = 99.
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) Right: 18 + 81 = 99.
- (b) 100 would include a number with no 4 or two 4s.
- (c) 110 overcounts, perhaps by counting numbers with two 4s.
- (d) 120 overcounts.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2009, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.