CAT 2025 Surds and Indices Question (Hard)

Question

The sum of digits of the number 625 65 times 128 36 , is

Accepted Answer

625 5 4 and 128 2 7 So, 625 65 , 128 36 5 260 ,2 252 2 252 5 252 cdot5 8 10 252 cdot5 8 Thus, the number equals 5 8 followed by 252 zeros. Now 5 8 390625 , and the sum of the digits of 390625 is 3 9 0 6 2 5 25. Zeros add nothing, so the required sum of digits is 25.

CAT 2025

Quantitative

Surds and Indices

Hard

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

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