Number System Question 4 - CAT 2025

Step-by-Step Explanation

• Analyze the subtraction block:

Look at the behavior of subtracting 123 from a power of 10:

• 10³ - 123 = 877
• 10⁴ - 123 = 9877
• 10⁵ - 123 = 99877

Following this induction rule, the value of 10²⁵ - 123 produces a 25-digit integer where the final three digits are fixed as 877, and the remaining (25 - 3) = 22 preceding digits are all 9s.

• Incorporate the higher order power:

Adding 10⁵⁰ places a single 1 at the 51st position value. Because this is well beyond the 25-digit span of our subtraction block, the two segments do not overlap, and the space between them is filled with zeros.

Non-zero components = one 1, twenty-two 9s, one 8, and two 7s

Sum of digits = 1 + (22 × 9) + 8 + (2 × 7) = 1 + 198 + 8 + 14 = 221

Correct Option: B