Brent@GMATPrepNow wrote:

Premalatha Anand wrote:If X and Y are positive integers and x/y has a remainder of 5, what is the smallest possible value of XY?


Ans is 30
Remainder cannot be larger than Y, so Y should be at least 6.

But my que is how can the smallest possible value of X can be 5??

Please explain!

There a two important rules regarding remainders

#1) If N divided by D, leaves remainder R, then 0 < R < D

#2) If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

IMPORTANT: Notice that 1 is the smallest possible value of k. A lot of people miss this. However, 1 divided by 5 equals 0 with remainder 1. In other words, 5 divides into 1 zero times with remainder 1.

For this question, we're told that x divided by y has a remainder of 5. So, the possible values of x are: 5, 5 + y, 5 + 2y, 5 + 3y, 5 + 4y, etc.

So, the SMALLEST value of x is 5.
For the division (x divided by y) leaves a remainder of 5, y must be greater than 5.
So, the SMALLEST value of y is 6

So, the SMALLEST value of xy = (5)(6) = 30

Cheers,
Brent