Help with a Math Problem from MGMAT Number properties book

bchekuri wrote:Hello everyone,

I just started studying for the GMAT. I am doing the MGMAT number properties currently and i am kinda stuck with this problem. The problem is on Page 134, problem no 24. The answer says 30. however i am getting 66.

Here is the problem...



If x and y are positive integers and x/y has a remainder of 5, what is the smallest possible value of xy?


Thanks for the help,
Bharath

In the future, please post answer choices as well.

In order to get a remainder of 5, we need to divide by a number bigger than 5.

Here's the general rule: if you're dividing an integer by integer n, there are n possible remainders, ranging from 0 to (n-1).

So, y must be at least 6; since we want to minimize xy, let's pick y=6.

Now we need to find the numerator: what's the smallest value of x so that x/6 has a reminder of 5?

Well, 1/6 would be 0rem1; 2/6 would be 0rem2; 3/6 would be 0rem3; 4/6 would be 0rem4; 5/6 would be 0rem5.. bingo!

So, the smallest values we can pick are x=5 and y=6, giving us xy=30.

If you got 66, you chose 11 and 6, forgetting that our minimum quotient is 0, not 1.

Thank you Stuart .. very clear explanation !
Silvia