Question

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

Answer 1

see a solution step below;

Explanation:

Method 1

A simple rule of thumb is;

`"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 xx x + 6 = k`

`7x + 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;

`((7x+5)+2)/y`

`(7x+7)/y`

`7 and 1` will divide `7x and 7` respectively without any remainder..

Therefore the remainder is `0` when `y = 7 or 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;

`k/7 = 13/7`, to have remainder `6`, hence making `k = 13`

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

Therefore, `(k + 2)/7 = (13 + 2)/7 = 15/7` to give a remainder `0`