2020 CSAT, all questions
UPSC Prelims 2020 · CSAT
Question 56: Basic Numeracy
What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?
a50
b25
c5
d1
AnswerUPSC’s answer is (a).
Only the last two digits matter, so reduce at each step modulo 100: 51 × 27 = 1377 leaves 77; 77 × 35 = 2695 leaves 95; 95 × 62 = 5890 leaves 90; 90 × 75 = 6750 leaves 50. Check: the product is divisible by 25 (from 75) and by 2 (from 62), so by 50, and it has only one factor of 2, so it is not divisible by 100. Remainder 50.
Why each option is right or wrong
- (a) Right: 6750 leaves 50.
- (b) The product is even, and a remainder of 25 would make it odd.
- (c) A remainder of 5 would make the product odd; it is even because of 62.
- (d) A remainder of 1 would make the product odd.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.