Question

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

• A. $13$
• B. $169$
• C. $11$
• D. $27$

Answer 1

The correct option is D $27$

Let the number be$X=47Q+11$
Let us find the square of X. So, it is $X^2=2209Q^2+517Q+121$
Here, the remainder when 121 is divided by 47 is 27.
Here, the remainder when $517Q$ is divided by $47$ for any value of $Q$ is $0$ as $517$ is divisible by $47.$
Here, the remainder when $2209Q^2$ is divided by $47$ for any value of $Q$ is $0$ as $2209$ is divisible by $47.$
Hence, the remainder will always be $27.$