UPSC Prelims 2007 · General Studies
Question 142: Basic Numeracy
Each of the 3 persons is to be given some identical items such that the product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done?
AnswerThe answer is (c).
The product 30 = 2 x 3 x 5 has three distinct prime factors, and each person's number is a product of some of them. Give each prime to one of the three persons: 3 choices for each of 3 primes, so 3 x 3 x 3 = 27 ordered ways. For example (1, 1, 30), (1, 2, 15), (2, 3, 5) and their orderings.
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) 21 undercounts; the total is 27.
- (b) 24 undercounts; the total is 27.
- (c) Correct: 3^3 = 27.
- (d) 33 overcounts; the total is 27.
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.