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
