1996 General Studies, all questions

UPSC Prelims 1996 · General Studies

Question 138: Basic Numeracy

If A = x² − y², B = 20 and x + y = 10, then

aA is greater than B
bB is greater than A
cA is equal to B
dIt is not possible to compare A and B as the data provided is inadequate

AnswerThe answer is (d).

A = x^2 - y^2 = (x + y)(x - y) = 10(x - y). Its value depends on x - y, which is not given, so A can be more than, equal to or less than B = 20: for example, x - y = 1 gives 10, and x - y = 4 gives 40. The data are inadequate for a comparison.

Why each option is right or wrong
  • (a) A = 10(x - y) can be less than 20 for some values.
  • (b) A can be greater than 20 for some values.
  • (c) A equals 20 only if x - y = 2, which is not given.
  • (d) Right: x - y is unknown, so A and B cannot be compared.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 1996, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.