SOLUTION: Two different numbers when divided by the same divisor, left remainders 11 & 21 respectively.When their sum was divided by the same divisor , remainder was 4.What is the divisor ?

Question 1045027: Two different numbers when divided by the same divisor, left remainders 11 & 21 respectively.When their sum was divided by the same divisor , remainder was 4.What is the divisor ?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

(Sorry about the typo):
We are told that
, and
.
So, adding up those two equations, we get

Since we are also told that
,
subtracting from the equation above from

we get

Since all the numbers involved in that equation are integers,
that tells us that is a factor of ,
and it has to be a factor larger than ,
because was a remainder,
and remainders are always smaller than their divisor.
The only factor of that is greater than is ,
so is the divisor.

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