PS: Number Properties from GMAT Prep

[swapna]

Could you help me with the following DS from GMAT prep.

If x and y are integers greater than 1, is x a multiple of y?
a) 3y^2 + 7y = x

b) x^2-x is a multiple of y

[mithunsam]

Statement 1
3y^2 + 7y = x
y(3y + 7) = x

Since y is an integer, 3y + 7 will be an integer, say I

Therfore, we can re-write the equation as
yI = x, where I is an integer
Hence, x is a multiple of y. Sufficient

Statement 2
x^2 - x is a multiple of y

We can re-write the statement as
x^2 - x = yI, where I is some integer
x(x-1) = yI
x = yI/(x-1)
For x to be a multiple of y, x-1 has to be a factor of I. But, we do not know anything about I or x-1. Insufficient

Answer is A

[jnelson0612]

Great job!

Note that statement two can be quickly evaluated and found insufficient by testing numbers.

For example, I can use 2 for x and y and obtain the answer YES, and use 4 for x and 3 for y and obtain the answer NO.