2018 CSAT, all questions
UPSC Prelims 2018 · CSAT
Question 23: Basic Numeracy
If X is between -3 and -1, and Y is between -1 and 1, then X^2 - Y^2 is in between which of the following?
a-9 and 1
b-9 and -1
c0 and 8
d0 and 9
AnswerUPSC’s answer is (d).
X lies between -3 and -1, so X² lies between 1 and 9 (squaring removes the sign). Y lies between -1 and 1, so Y² lies between 0 and 1. The expression X² - Y² is therefore always above 1 - 1 = 0 and can approach 9 - 0 = 9. It lies between 0 and 9. Check an extreme: X = -2.9, Y = 0 gives 8.41, which is above 8, so 0 and 8 is too narrow.
Why each option is right or wrong
- (a) The expression can never be negative, and it can exceed 1 easily.
- (b) Negative values are impossible because X² > 1 > Y².
- (c) Too narrow: X = -2.9, Y = 0 gives 8.41.
- (d) Correct: X² - Y² ranges from just above 0 to just below 9.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.