UPSC Prelims 2007 · General Studies
Question 136: Basic Numeracy
Amit has five friends: 3 girls and 2 boys. Amit’s wife also has five friends: 3 boys and 2 girls. In how many maximum different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s friends?
AnswerThe answer is (c).
Split by what Amit's two guests are. Amit's friends: 3 girls, 2 boys; his wife's: 3 boys, 2 girls. If Amit supplies 2 boys, the wife supplies 2 girls: 1 x 1 = 1. If Amit supplies 2 girls (3 ways), the wife supplies 2 boys (3 ways): 9. If Amit supplies 1 boy and 1 girl (2 x 3 = 6), the wife also supplies 1 boy and 1 girl (3 x 2 = 6): 36. Total 1 + 9 + 36 = 46.
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) 24 misses cases; the total is 46.
- (b) 38 misses cases; the total is 46.
- (c) Correct: 1 + 9 + 36 = 46.
- (d) 48 overcounts; the total is 46.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2007, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.