UPSC Prelims 2018 · CSAT

Question 77: Basic Numeracy

If x - y = 8, then which of the following must be true?

1.Both x and y must be positive for any value of x and y.
2.If x is positive, y must be negative for any value of x and y.
3.If x is negative, y must be positive for any value of x and y.

Select the correct answer using the code given below.

a1 only

b2 only

cBoth 1 and 2

dNeither 1 nor 2 nor 3

AnswerUPSC’s answer is (d).

Test each statement with values satisfying x - y = 8. Statement 1: x = 5, y = -3 works and y is negative, so both need not be positive. Statement 2: x = 10, y = 2 works and y is positive though x is positive, so y need not be negative. Statement 3: if x is negative then y = x - 8 is also negative, so y is never positive here. All three fail, so none is true. A single counter-example is enough to refute a 'must be true' claim.

1. x = 5, y = -3 gives a negative y.
2. x = 10, y = 2 gives a positive y with positive x.
3. If x is negative, y = x - 8 is negative too.

Why each option is right or wrong

(a) Statement 1 fails for x = 5, y = -3.
(b) Statement 2 fails for x = 10, y = 2.
(c) Both statements 1 and 2 fail.
(d) Correct: each statement has a counter-example.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.