CDS 2026 (I) Elementary Mathematics, question 5

Topic: Number system

Answers by SolvedPaper. UPSC has not released the official answer key for this paper yet. We will update it when they do.

Q5

Let P=55×1515×2525×3535P=5^{5}\times 15^{15}\times 25^{25}\times 35^{35} and Q=1010×2020×3030×4040Q=10^{10}\times 20^{20}\times 30^{30}\times 40^{40}. What is the number of consecutive zeros at the end of the sum (P+Q)(P+Q) ?

  1. (a) 100100
  2. (b) 6565
  3. (c) 5050
  4. (d) ZeroCorrect answer

Solution.

Answer: (d) Zero

  1. Every factor of P is odd and divisible by 5, so P ends in 5.
  2. Every factor of Q is a multiple of 10, so Q ends in 0.
  3. Therefore P+QP + Q ends in 5 and has no trailing zero.
  4. Shortcut: Check the units digit before counting factors of 2 and 5; that counting method applies directly to a product, not to a sum.