Data Sufficiency

[email protected] wrote:If xy=-15 , what is the value of xy(x-y)?

1)x+y=2
2)x^2y=45

Can we solve it with statement 1 independently with this method?

xy(x-y)= x^2y-xy^2 now if we multiply the whole with -1 it will become= -1(x^2y - xy^2), now if we take -xy as common wont the value within the bracket become (x+y), now
since we know that xy =-15 therefore - xy =15 and statement 1 gives us the value of x+y, hence we can solve the equation!

Good idea, but the conclusion you made in green is not correct.

Let's start with the part where you got (-1)(x^2y - xy^2)
If we factor -xy out, we get: (-1)(-xy)(-x + y)
In your solution, you got (x + y), which is not correct.

Cheers,
Brent

[email protected] wrote:If xy = -15, what is the value of xy(x - y)?

1)x + y = 2
2)x²y = 45

Target question: What is the value of xy(x - y)?

Given: xy = -15

IMPORTANT:Since xy = -15, then we already know part of the value of xy(x - y). So, all we need to do here is determine the value of(x - y). If we can find the value of (x - y), we can find the value of xy(x - y). So, let's rephrase the target question . . .

Rephrased target question: What is the value of (x - y)?

Statement 1: x + y = 2
Rearrange to get: x = 2 - y
Now take our given equation (xy = -15), and replace x with 2-y to get:
(2 - y)y = -15
Expand: 2y - y² = -15
Rearrange: y² - 2y - 15 = 0
Factor: (y - 5)(y + 3) = 0
So, y = 5 or -3
If y = 5, then x = -3 (since x + y = 2), which means x - y = -8
If y = -3, then x = 5 (since x + y = 2), which means x - y = 8
Since we cannot answer the rephrased target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x²y = 45
In other words, x(xy) = 45
Since we already know that xy = -15, we know that x must equal -3
Now that we know that x = -3, we can use the fact that xy = -15, to conclude that y = 5.
At this point, we know that x - y = (-3) - 5 = -8
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

faraz_jeddah wrote: if x = -3 should that not make y = 5 since the question stem tells us xy = -15?

You're absolutely right. Good catch!

I've edited my solution accordingly.

Thanks and cheers,
Brent