Problem Solving

gmatisgay wrote:If xy ≠ 0, what is the value of 1/x + 1/y?
(1) 1 / (x+y) = -1
(2) xy = 6(x+y)

This is a great example of the utility of rewording the target question before examining the statements.

If we add 1/x + 1/y, we get y/xy + x/xy which equals (x+y)/xy

So, we can reword the target question as "What is the value of (x+y)/xy?"

Statement 1:
If 1/(x+y) = -1, we know that (x+y)=-1
Is this enough information to find the value of (x+y)/xy?
No. If we replace (x+y) with -1, we get -1/xy
Since we still don't know the value of xy, we cannot answer the target question with certainty, so statement 1 is NOT SUFFICIENT

Statement 2:
If xy = 6(x+y), we can take the new target question and replace xy with 6(x+y) to get (x+y)/6(x+y), which simplifies to be 1/6
Since we are able to answer the target question with certainty, statement 2 IS SUFFICIENT and the answer is B

Cheers,
Brent

EddieU wrote:Hi Brent, your calculations make totally sense. Can you please help me find my mistake in my thoughts?

what if we did not do anything with the question first? How come (1) is insufficient?

we have 1/x + 1/y=?

and they gave us the information 1/(x+y)= -1. if we multiply both sides with (x+y) we get 1 = -x-y if we add x to both sides we get x = -y. if we now substitute x with -y for the equation above, we get 1/-y + 1/y which is equal to -1/y + 1/y and this is equal to 0.

Where is the mistake?

Thanks in advance

If we arrange your calculations vertically, you'll see the slight error:

1/(x+y)= -1
Multiply both sides with (x+y) to get 1 = -x-y
Add x to both sides we get x = -y

If we add x to both sides we get 1+x = -y

Cheers,
Brent