Question

A number $x$ when divided by $7$ leaves a remainder $1$ and another number $y$ when divided by $7$ leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

We know that,

$Dividend=(Divisor\times Quotient)+Remainder$

Given numbers $x,y$

Let us assume $a$ is the quotient when $x$ is divided by $7$ and $b$ is the quotient when $y$ is divided by $7$

$x=7$ $\times$$a+1$ and $y=7$ $\times$$b+2$

$\therefore$ $x+y=7a+7b+1+2=7(a+b)+3$

$\Rightarrow$$(x+y)$ when divided by $7$ leaves a remainder $3$.