Question

When a positive integer $y$ is divided by $47,$ the remainder is $11$. Therefore, when $y^2$ is divided by $47$, the remainder will be

• A. $7$
• B. $17$
• C. $27$
• D. $37$

Answer 1

Answer: (C)

$27$

Let the positive integer be y

Now $y=47x+11$

$y^2=(47x+11{)}^2$

$=47x\times 47x+2\times 47\times 11+121$,

The first 2 terms are divisible by 47, we check the 3rd term for remainder.

$121=47\times 2+27$

The remainder is 27.