Civil Services Prep

Prelims 2026 · CSAT / Quantitative Aptitude · Question 19

If 10^m × 1000 × n = 75^25 × 25^32 × 32^75, where n is not divisible by 10, then the value of m is<br/>

  1. 101
  2. 111
  3. 121
  4. 131

Answer

111

75^25 × 25^32 × 32^75 = (3×5^2)^25 × (5^2)^32 × (2^5)^75 = 3^25 × 5^114 × 2^375. So total factors of 10 = min(114, 375) = 114. Since 1000 = 10^3, we get m + 3 = 114, so m = 111.

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