UPSC Prelims 2010 · General Studies
Question 112: Basic Numeracy
A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4th full ?
AnswerThe answer is (d).
The number of eggs doubles each day, since the number added equals the number already in the basket. So the basket was half full on day 23 (one day before it was full) and a quarter full on day 22 (two days before). Check: a quarter on day 22 becomes a half on day 23 and is full on day 24. Remember: with daily doubling, count backwards from the full day; each step back halves the quantity.
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) Day 6 would be 1/2^18 of the full basket.
- (b) Day 12 would be 1/2^12 of the full basket.
- (c) Day 17 would be 1/2^7 of the full basket.
- (d) Right: day 22 is two doublings before day 24, so 1/4 full.
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.