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If xy does not equal zero, what is the value of xy

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Source: — Data Sufficiency |
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by mbawisdom » Wed Mar 07, 2018 4:21 pm
lheiannie07 wrote:If xy does not equal zero, what is the value of xy?

(1) 2/x + 2/y = 3
(2) x^3 - (2/y)^3 = 0

What's the best way to determine the sufficient statement?

OA B
Look at statement (1) first:

2/x + 2/y = 3
(2y + 2x)/xy = 3
xy = 2(x + y)/3

We don't know x + y so we can't solve for xy --> NOT SUFFICIENT!

Look at statement (2) second:

x^3 - (2/y)^3 = 0
x^3 - 8/y^3 = 0
(xy)^3 - 8 = 0
(xy)^3 = 8
xy = 2

SUFFICIENT

Where did you get stuck?
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by GMATGuruNY » Thu Mar 08, 2018 3:29 am
lheiannie07 wrote:If xy does not equal zero, what is the value of xy?

(1) 2/x + 2/y = 3
(2) x^3 - (2/y)^3 = 0
Statement 1: 2/x + 2/y = 3
2/x = 3 - 2/y

Case 1: y=1
Plugging y=1 into 2/x = 3 - 2/y, we get:
2/x = 3 - (2/1)
2/x = 1
2 = x
xy = 2*1 = 2.

Case 2: y=-1
Plugging y=-1 into 2/x = 3 - 2/y, we get:
2/x = 3 - (2/-1)
2/x = 5
2/5 = x
xy = (2/5)(-1) = -2/5.

Since xy can be different values, INSUFFICIENT.

Statement 2: x³ - (2/y)³ = 0
x³ = (2/y)³
x = 2/y
xy = 2.
SUFFICIENT.

The correct answer is B.
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