Question

If R and S are different integers both divisible by $5$, then which of the following is not necessarily true?

• A. $(R-S)$ is divisible by $5$
• B. $(R+S)$ is divisible by $5$
• C. $(R^2+S^2)$ is divisible by $5$
• D. $(R+S)$ is divisible by $10$

Answer 1

The correct option is D $(R+S)$ is divisible by $10$

Let the numbers be $R=5m$ and $S=5n,$

m, n being integers.

Then
$R+S=5m+5n=5(m+n)$
which is divisible by $5$
$R-S=5m-5n=5(m-n)$
which is divisible by $5$

$R^2+S^2=25m^2+25n^2=25(m^2+n^2)$
Which is divisible by $5$
suppose we take$m=2$ and $n=3$ then $R+S=5(2+3)=25$
which is not divisible by $10$