Advance GMAT Quant Try-It #3-1

[a.sarwari]

Hi,

The question states:

If x and y are integers and 4xy = x^2y+4y, what is the value of xy?
1) y-x = 2
2) x^3<0

I am really confused here because why can't you just simplify by factoring a 'y' from the right side of the equation, cancel 'y' from both sides of the equation and finally conclude that "x=2."

I understand that this solution will yield 8y=8y when you plug '2' back into the original equation (aka "all real solution")

My question is: Is there something wrong with my algebra or is this a bad question? Please explain and guide me so I know when to cancel out a variable and when not to.

Thanks in advance.

[mithunsam]

We cannot cancel variables (unless you know values and/or signs) here because we don't know their values. For example, you cancelled y from both sides of the equation and got x=2. But, what if y = 0? Then x could be -1, 0, 1, 2, 3, or any other number.

One way to solve the question is to factorize it.

x^2y-4xy+4y=0
y(x^2-4x+4) =0
y(x-2)^2 = 0
y = 0 or x-2 = 0
y = 0 or x = 2

1) y-x = 2 insufficient (because we don't know anything about x or y)
2) x^3<0 sufficient (because by factorizing the equation, we know either x = 2 or y =0. So if x is -ve, then y has to be 0)

Answer should be B

[a.sarwari]

This is the exact explanation in the book, which did not help in the first place. Instructors - please shed some light!

[mithunsam]

Sorry! I didn't know how it was solved in the book. Not everyone has this book.

I am not sure, other than factorization, whether there is another way to solve this problem.

One thing you need to keep in mind is that "variables cannot be cancelled unless you know the sign" Period!

Here you haven't stated whether x & y are +ve, -ve or 0. So, we cannot cancel variables.

Therefore, the simplest way to rewrite the equations is y(x-2)^2 = 0 (explained in my previous post)

This will yield two solutions y =0 & x=2.

[tim]

a.sarwari, can you let us know what specific steps you had trouble with in the book's explanation? that may help us come up with an explanation that will make sense to you..