Question

If x and y are intergers divisible by 5, then which of the following is not necessarily true?

• A. $x-y$ is divisible by 5
• B. $x^2-y^2$ is divisible by 25
• C. $x+y$ is divisible by 10
• D. None of these

Answer 1

The correct option is C $x+y$ is divisible by 10

Let the integer $x=5$ and $x=10$

$A.$ $x-y$ is divisible by $5.$

$\Rightarrow$ $x-y=5-10=-5$

$\Rightarrow$ Here, $-5$ is divisible by $5$

$\therefore$ This statement is true.

$B.$ $x^2-y^2$ is divisible by $25$

$\Rightarrow$ $x^2-y^2=(5{)}^2-(10{)}^2$

$=25-100$

$=75$

So, $75$ is divisible by $25$.

$\therefore$ This statement is also true.

$C.$ $x+y$ is divisible by $10$

$\Rightarrow$ $x+y=5+10=15$

$\Rightarrow$ $15$ is not divisible by $10$

$\therefore$ This statement is also False.