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#