2021 CSAT, all questions

UPSC Prelims 2021 · CSAT

Question 63: Basic Numeracy

There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?

a1
b2
c3
d4

AnswerUPSC’s answer is (b).

Let PQ = 3 and QR = 5. The points are on a line, so R can lie on either side of Q. If R is beyond Q, away from P, then PR = 3 + 5 = 8 and PQ : PR = 3 : 8. If R lies on P's side of Q, then PR = 5 − 3 = 2 and PQ : PR = 3 : 2. These are two different ratios, so n = 2. Remember: for collinear points, always consider both orderings.

Why each option is right or wrong
  • (a) Counts only one ordering; R can be on either side of Q.
  • (b) Right: PQ : PR is 3 : 8 or 3 : 2.
  • (c) No third arrangement exists on a line.
  • (d) Only two positions of R relative to Q are possible, so four ratios cannot arise.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.