jainrahul1985 wrote:If xy ≠ 0, could y be expressed as -2/x?

(1) x^2y^2 - xy = 6

(2) y ≠ 3/x

OA A

Hi jainrahul1985!

This is a tricky little quadratic problem but it looks like the OA is actually incorrect so I'm very glad you PM'd me about it! Can you post the original source and also check to verify that the OA of A is correct - it should be C.

Let's start the same way we should begin every DS problem, by rephrasing the question into something we can work with!

First, we are told that xy ≠ 0, so that means neither x nor y = 0! This is good to know. Now, the question asks:

Does y = -2/x?
Well, let's multiply both sides by x to get that variable out of the denominator:

Does xy = -2?

This is a bit easier to ask, so I think we have sufficiently rephrased. Now on to the statements.

**Statement (1): x^2y^2 - xy = 6
Notice that we have squared variables and non-squared variables, so we should immediately begin to think about quadratics (problems with x^2 and x typically). To solve quadratics, we typically want to have everything set =0, so let's start there:

x^2y^2 - xy - 6 = 0

Now, the un-squared "middle" term contains BOTH an x and a y. So let's lump the first term x and y together. Since the exponents on the x and y are the same, we can actually do the multiplication first (x^2y^2 = (xy)^2):

(xy)^2 - xy - 6 = 0

Now this is starting to look a lot more like a typical quadratic, but instead of a simple x^2 or z^2 or whatever, we have a combo term (xy)^2. To make this easier to see, let's use a little substitution magic and simply call xy = z. Now we can rewrite:

z^2 - z - 6 = 0

Well this looks a lot easier to factor:

(z-3)(z+2) = 0
z = 3, or z = -2.

And since we said that z=xy, then
xy=3, or xy=-2.

But this is not enough to say that xy=-2 (because it could also equal 3), Insufficient, Eliminate A and D from the choices

**Statement (2): y ≠ 3/x
From this, all we know is that the product xy≠3, but this is not enough to say that it does = -2, Insufficient, Elminate Choice B

**Statement (1+2):
From (1) we know that xy could equal either 3 or -2, but from (2) we know that it cannot equal 3, so it must =-2. Sufficient, the correct choice is C

Hope this helps!

Whit

jainrahul1985 wrote:If xy ≠ 0, could y be expressed as -2/x?

(1) x^2y^2 - xy = 6

(2) y ≠ 3/x

OA A

I don't think this could ever be a GMAT question - too many problems with the word "could."

Even without using any of the statements, it's possible that y = -2/x

Analogous example: Juan is thinking of an integer between 1 and 10. Could the integer be 7? Sure!

I believe the intent of the question was to have students take x^2y^2 - xy = 6 and set it equal to zero (x^2y^2 - xy - 6 = 0) and then factor it to get (xy-3)(xy+2)=0, with the idea that xy+2 could equal zero, in which case y = -2/x. However, xy+2 could equal zero WITHOUT using statement 2.

I think it might be best to disregard this question.

What's the source?

Cheers,
Brent

Aside: all DS questions are impossible to answer without using the statements.

For example: If ABC is a triangle, is the area of ABC = 12?
Well, maybe the area equals 12 and maybe it doesn't. We need more info.

Alternatively, consider the question: If ABC is a triangle, could the area of ABC = 12?
There's nothing in the given information that would suggest that the area cannot equal 12. So, at this point (without even looking at any statements), it seems reasonable to conclude that the area could equal 12.

The same applies to the original question.

Now if the target question were"does y = -2/x," then I'd agree with Whitney and say that the answer is C.

Cheers,
Brent

Brent@GMATPrepNow wrote:

jainrahul1985 wrote:If xy ≠ 0, could y be expressed as -2/x?

(1) x^2y^2 - xy = 6

(2) y ≠ 3/x

OA A

I don't think this could ever be a GMAT question - too many problems with the word "could."

Completely Agree Brent! A search of all 12th Ed OG problems and 2nd Ed Quant Supplement problems and NO DS problems use the word "could" in this context. I second my request for the original source.


Whit