# When a positive integer k is divided by 7, the remainder is 6. What is the remainder when k+2 is divided by?

Mar 5, 2018

see a solution step below;

#### Explanation:

Method 1

A simple rule of thumb is;

$\text{factor" xx "divisor" + "remainder" = "the integer}$

Therefore according to the question, the integer is $k$, divisor is $7$ , let the factor be $x$

So;

$7 \times x + 6 = k$

$7 x + 5 = k$

We can say let the unknown we are dividing by be represented with $y$

When $k + 2$ is divided by $y$ then the expression becomes;

$\frac{\left(7 x + 5\right) + 2}{y}$

$\frac{7 x + 7}{y}$

$7 \mathmr{and} 1$ will divide $7 x \mathmr{and} 7$ respectively without any remainder..

Therefore the remainder is $0$ when $y = 7 \mathmr{and} 1$

Method 2

We can also use instincts..

Now we are looking for a number that will divide $7$ to give a reminder of $6$

We have $13$ as that number;

$\frac{k}{7} = \frac{13}{7}$, to have remainder $6$, hence making $k = 13$

Now if, $K + 2$ to give a remainder of $0$;

Therefore, $\frac{k + 2}{7} = \frac{13 + 2}{7} = \frac{15}{7}$ to give a remainder $0$