UPSC Prelims 2014 · CSAT
Question 7: Basic Numeracy
A group of 630 children is seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible ?
AnswerUPSC’s answer is (d).
Rows fall by 3 each time. With n rows and a children in the first row, the total is n(2a - 3n + 3)/2 = 630, so n(2a - 3n + 3) = 1260. For n = 3, a = 213; for n = 4, a = 162; for n = 5, a = 132, all whole numbers. For n = 6 you get 2a = 225, which is not a whole number, so six rows cannot work. Test each option's n this way.
Why each option is right or wrong
- (a) Possible: rows of 213, 210 and 207 add to 630.
- (b) Possible: rows of 162, 159, 156 and 153 add to 630.
- (c) Possible: rows of 132, 129, 126, 123 and 120 add to 630.
- (d) Not possible: six rows would need the first row to have 112.5 children.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2014, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.