CAT 2025

Slot 2

QA

Question & Solution

$$625=5^4$$ 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.