UPSC Prelims 2020 CSAT Paper II · Q56 of 80 Basic Numeracy medium

What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?

  1. (a) 50 ✓ UPSC's answer
  2. (b) 25
  3. (c) 5
  4. (d) 1

Why the answer is (a)

• To find the remainder when a product is divided by 100, we can determine the last two digits of the product.

• First, calculate the product of the first two numbers: 51 × 27 = 1377, which ends in 77.

• Next, multiply this result by the third number: 77 × 35 = 2695, which ends in 95.

• Then, multiply this result by the fourth number: 95 × 62 = 5890, which ends in 90.

• Finally, multiply this result by the last number: 90 × 75 = 6750, which ends in 50.

• Since the last two digits of the total product are 50, the remainder when divided by 100 is 50.

Why the other options are wrong

(b) 25
The last two digits of the product are 50, not 25, so the remainder is not 25.
(c) 5
The last two digits of the product are 50, not 05, so the remainder is not 5.
(d) 1
The last two digits of the product are 50, not 01, so the remainder is not 1.

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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