UPSC Prelims 2021 · CSAT
Question 70: Basic Numeracy
An amount of money was distributed among A, B and C in the ratio p : q : r. Consider the following statements :
- 1.A gets the maximum share if p is greater than (q + r).
- 2.C gets the minimum share if r is less than (p + q).
Which of the above statements is/are correct ?
AnswerUPSC’s answer is (a).
Shares are proportional to p, q and r, all positive. Statement 1: if p > q + r, then p > q and p > r, since q and r are positive, so A gets the maximum share. True. Statement 2: r < p + q does not make C smallest; take p = 1, q = 1, r = 1.5: r < p + q = 2, yet C gets the largest share. False. Only 1 is correct. Remember: 'less than the sum of the other two' says nothing about being the smallest; test with numbers.
- 1. If p > q + r then p exceeds both q and r, so A gets the most.
- 2. In the ratio 1 : 1 : 1.5, r is less than p + q, but C gets the largest share.
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: If p > q + r then p exceeds both q and r, so A gets the most.
- Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: In the ratio 1 : 1 : 1.5, r is less than p + q, but C gets the largest share.
Only (a) is left. This one needs every statement.
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) Right: p > q + r means A's share exceeds each of the others.
- (b) Statement 2 fails: with 1 : 1 : 1.5, r < p + q, yet C gets the most.
- (c) Statement 2 is false, so both cannot be correct.
- (d) Statement 1 is true, so this fails.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.