UPSC Prelims 2020 CSAT Paper II · Q50 of 80 Basic Numeracy easy

What is the largest number among the following?

  1. (a) (1/2)^-6
  2. (b) (1/4)^-3
  3. (c) (1/3)^-4 ✓ UPSC's answer
  4. (d) (1/6)^-2

Why the answer is (c)

• To compare the numbers, convert each expression with a negative exponent into a positive power by inverting the base fraction.

• Option (a) (1/2)^-6 becomes 2^6, which equals 64.

• Option (b) (1/4)^-3 becomes 4^3, which equals 64.

• Option (c) (1/3)^-4 becomes 3^4, which equals 81.

• Option (d) (1/6)^-2 becomes 6^2, which equals 36.

• Comparing the calculated values (64, 64, 81, and 36), 81 is the largest number, so option (c) is the correct answer.

Why the other options are wrong

(a) (1/2)^-6
The value of (1/2)^-6 is 64, which is smaller than the value of option (c), which is 81.
(b) (1/4)^-3
The value of (1/4)^-3 is 64, which is smaller than the value of option (c), which is 81.
(d) (1/6)^-2
The value of (1/6)^-2 is 36, which is the smallest among all the given options.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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