UPSC Prelims 2009 · General Studies
Question 106: Basic Numeracy
In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. Consider the following statements :
- 1.The total number of students that participated in the competition is 30.
- 2.The number of games in which both players were girls is 78.
Which of the statements given above is/are correct ?
AnswerThe answer is (c).
Boy-girl games number m x n = 221 = 13 x 17. With m > n > 1, m = 17 and n = 13. The total number of students is 17 + 13 = 30, so statement 1 is correct. Games with both players girls: 13C2 = 13 x 12 / 2 = 78, so statement 2 is correct too.
- 1. m = 17 and n = 13, so there are 30 students.
- 2. Girl-girl games are 13C2 = 78.
How you could have got this
- If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: m = 17 and n = 13, so there are 30 students.
- Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.
What you needed to know: Girl-girl games are 13C2 = 78.
Only (c) is left. This one needs every statement.
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) Wrong: statement 2 is also correct.
- (b) Wrong: statement 1 is also correct.
- (c) Right: both statements are correct.
- (d) Wrong: both statements are correct.
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.