CAT 2025 Slot 2 QA Q20 Number Systems

Question 20 of the Quantitative Ability (QA) section, CAT 2025 Slot 2, with CAT's official answer and a worked solution.

The sum of digits of the number \( ( 625 ) ^ { 65 } \times ( 128 ) ^ { 36 } \), is

TITA: type in the answer. There are no options and no negative marking.

Answer: 25 Number Systems TITA

Solution

  1. \(625^{65} = 5^{260}\) and \(128^{36} = 2^{252}\).
  2. Product \(= 10^{252} \times 5^{8} = 390625 \times 10^{252}\).
  3. Digit sum \(= 3 + 9 + 0 + 6 + 2 + 5 = 25\).

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