2009 General Studies, all questions
UPSC Prelims 2009 · General Studies
Question 95: Basic Numeracy
A person has 4 coins each of different denomination. What is the number of different sums of money the person can form (using one or more coins at a time)?
a16
b15
c12
d11
AnswerThe answer is (b).
Each coin is either used or left out, giving 2 x 2 x 2 x 2 = 16 combinations. Remove the case where no coin is used, leaving 16 - 1 = 15 sums, taking every sum as different (as with denominations like 1, 2, 5, 10). The general rule: n coins give 2^n - 1 non-empty selections.
Why each option is right or wrong
- (a) 16 counts the empty selection, which is not a sum of money.
- (b) Right: 2^4 - 1 = 15.
- (c) 12 is not the count of selections.
- (d) 11 is not the count of selections.
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.