UPSC Prelims 2020 · CSAT

Question 50: Basic Numeracy

What is the largest number among the following?

a(1/2)^-6

b(1/4)^-3

c(1/3)^-4

d(1/6)^-2

AnswerUPSC’s answer is (c).

A negative exponent flips the fraction, so (1/a)^-n = a^n. The four values are 2^6 = 64, 4^3 = 64, 3^4 = 81 and 6^2 = 36. The largest is 81, from (1/3)^-4. Do not judge by the base or the exponent alone: the first two tie at 64, and base 3 with exponent 4 beats both.

Why each option is right or wrong

(a) (1/2)^-6 = 64.
(b) (1/4)^-3 = 64.
(c) Right: (1/3)^-4 = 81.
(d) (1/6)^-2 = 36, the smallest.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.