Question

$50^{\text{th }}$ root of a number $x$ is $12$ and $50^{\text{th }}$ root of another number $y$ is $18$ . Then the remainder obtained on dividing $(x+y)$ by $25$ is_____

Answer 1

Answer: 23

$x+y=12^{50}+18^{50}=(150-6{)}^{25}+(325-1{)}^{25}$
$=25K-\left(6^{25}+1\right)=25K-\left((5+1{)}^{25}+1\right)$
$=25K_1-2$
Remainder $=23$