Question

Find the remainder value in the following expression
$\frac{{23}^2+{29}^2+{31}^2+{37}^2}{24}$

• A. $2$
• B. $17$
• C. $4$
• D. $3$

Answer 1

The correct option is A $2$

$\frac{(30-7{)}^2+(30-1{)}^2+(30+1{)}^2+(30+7{)}^2}{24}$

$\Rightarrow \frac{2\left[\right(30{)}^2+\left(7{)}^2\right]+2\left[\right(30{)}^2+1^2]}{24}$ $\left[\right(a-b{)}^2+(a+b{)}^2=2(a^2+b^2\left)\right]$

$\Rightarrow \frac{2(30{)}^2+7^2+1}{12}$

$\Rightarrow \frac{1800+49+1}{12}=\frac{150\left(12\right)+4\left(12\right)+1+1}{12}$

Remainder $=1+1=2$