CAT 2025 Slot 3 QA Q17 Number Systems

Question 17 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.

The sum of all the digits of the number \( \left( 10 ^ { 50 } + 10 ^ { 25 } - 123 \right) \), is
  1. A
    \( 324 \)
  2. B
    \( 221 \)
  3. C
    \( 212 \)
  4. D
    \( 255 \)

Answer: (B) 221 Number Systems MCQ

Solution

  1. \(10^{25} - 123 = (10^{25} - 1) - 122\): 25 nines with the last three \(999 - 122 = 877\), i.e. 22 nines followed by 877.
  2. Digit sum \(= 22 \times 9 + 8 + 7 + 7 = 220\).
  3. Adding \(10^{50}\) puts a leading 1 with zeros in between, so the total is 221.

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