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

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Answer 1 · 2018-03-05T14:11:52

see a solution step below;

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 $0$