Ozlemg wrote:If X and Y are integers, what is the value of XY?
(1) X3 - 3X2 - 2X - 8 = 0.
(2) 4 + 3Y = 2Y + 8.
How (1) is sufficent, i could not understand?
OA will come!
I'm assuming that statement 1 is supposed to read: X^3 - 3X^2 - 2X - 8 = 0
Statement 1:
Our first reaction to this might be to notice that, since there is no information about Y, we cannot find the value of XY.
However, if it were the case that X=0, then we
would be able to find the value of XY. It would be 0 (as long as zero is the
only possible value of X).
So, let's see if X=0 is a solution.
When we plug
0 into the equation we get
0^3 - 3(
0)^2 - 2(
0) - 8 = 0
When we simplify, we get -8 = 0
So, we can see that 0 is not a solution to the equation.
As such, we cannot find the value of XY, which means statement 1 is not sufficient.
Statement 2:
Here, there is no information about X, but if Y=0 then we can still find the value of XY
When we solve 4 + 3Y = 2Y + 8, we get Y=4
Since we don't know the value of X, we cannot find the value of XY.
So, statement 2 is not sufficient.
Statements 1&2:
At this point, I should mention that this question is
beyond the scope of the GMAT. Here's why:
The equation X^3 - 3X^2 - 2X - 8 = 0 is a cubic equation, and cubic equations can have 1, 2 or 3 solutions.
For this question, we need to determine whether or not this equation has exactly 1 solution.
If it has 1 solution for X, then the statements 1 and 2 combined is sufficient (since we would have exactly one value for X and one value for Y)
If the equation has 2 or 3 integer solutions for X, then the statements 1 and 2 combined is not sufficient.
Solving X^3 - 3X^2 - 2X - 8 = 0 for X is too much math for the GMAT. It's possible that you MIGHT have to solve a cubic equation on the GMAT (if you're on your way to a BIG score), but if you were to encounter such an equation, it would be much more manageable (i.e., much easier to factor).
This equation is too tough to solve and requires us to know things called the Factor Theorem and the Remainder Theorem. Plus you would need to know how to divide polynomials. All of these are beyond the scope of the GMAT.
That said, when we do apply the various theorems and techniques, we get:
X^3 - 3X^2 - 2X - 8 = 0
(X-4)(X^2+X+2)=0
This means that X-4=0, which means X=4.
And it means that X^2+X+2=0. When we try to solve this equation, we find that it is unsolvable (
hint: try applying the Quadratic Formula and you'll end up trying to find the square root of a negative number).
Since X^2+X+2=0 has no solution, we can see that there is only one solution for X (X=4), which means the statements combined are sufficient and the answer is
C
What's the source of this question?
Cheers,
Brent
