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DS:Inequalities

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DS:Inequalities

by psm12se » Tue Feb 04, 2014 5:10 pm
If xy > 0 does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

I solved this question and came out with answer as D but OA is A

Here is my approach

The question is asking whether (x-1)(y-1) = 1
so xy - x - y + 1 = 1
so xy = x + y ?

Statement 1: Says the same as the derived equation
Sufficient

Statement 2: x = y
substituted the values in the derived equation
x^2 = 2x
x^2 - 2x = 0
x(x-2) = 0
so x = 0 or x = 2
since xy > 0 so x = 2
Sufficient

Please let me know if the my approach is wrong here and how is statement 2 insufficient.
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by Mike@Magoosh » Tue Feb 04, 2014 6:03 pm
psm12se wrote:If xy > 0 does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

I solved this question and came out with answer as D but OA is A

Here is my approach

The question is asking whether (x-1)(y-1) = 1
so xy - x - y + 1 = 1
so xy = x + y ?

Statement 1: Says the same as the derived equation
Sufficient

Statement 2: x = y
substituted the values in the derived equation
x^2 = 2x
x^2 - 2x = 0
x(x-2) = 0
so x = 0 or x = 2
since xy > 0 so x = 2
Sufficient

Please let me know if the my approach is wrong here and how is statement 2 insufficient.
Dear psm12se,
I'm happy to respond. :-)

GMAT DS is very tricky. Under Statement #2, by assuming the equation about which they are asking and plugging in x = y, you are merely answering the question: is the equation (x - 1)(y - 1) = 1 consistent with the equation x = y? In other words, it is possible for both to be true at the same time? That's NOT the content of the sufficiency question.

The GMAT DS Sufficiency question is, very specifically: if we are told for a fact that x = y is true, from that fact, would we be able to deduce that (x - 1)(y - 1) = 1? In other words, can we start from x = y, and establish that (x - 1)(y - 1) = 1?

One way to go about it is with simple number-plugging. If x = y = 1, then (x - 1)(y - 1) = 1 doesn't work, but if x = y = 2, then it does. Two choices, two different answers. Not sufficient.

Statement #1 is sufficient because, as you found, it's the same equation.

Statement #2 is not sufficient.

OA = [spoiler](A)[/spoiler]

Does all this make sense?
Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by [email protected] » Wed Feb 05, 2014 1:26 am
Hi psm12se,

This DS question can be tackled by TESTing Values and tracking the results.

We're told that XY > 0, which means that neither variable can equal 0. We're asked does (X-1)(Y-1) = 1? This is a YES/NO question.

Fact 1: X + Y = XY

Since we're not allowed to use 0, this is a rather restrictive piece of information.
The only values that fit are X = 2, Y = 2
Plugging those values into the question, we find that the answer is YES.
Since that's the only answer, Fact 1 is SUFFICIENT

Fact 2: X = Y

If X = Y = 1, then the answer to the question is NO
If X = Y = 2, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Final Answer: A

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by GMATGuruNY » Wed Feb 05, 2014 3:40 am
psm12se wrote:If xy > 0 does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

Statement 2: x = y
substituted the values in the derived equation
x^2 = 2x
x^2 - 2x = 0
x(x-2) = 0
so x = 0 or x = 2
since xy > 0 so x = 2
Sufficient

Please let me know if the my approach is wrong here and how is statement 2 insufficient.
The portion in red misrepresents the problem.
There is NO EQUATION in the question stem.
Rather, there is only a QUESTION: Does (x-1)(y-1) = 1?

When we substitute x=y into this question, we get:
(x-1)(x-1) = 1?
x² - 2x + 1 = 1?
x(x-2) = 0?
Does x=0 or x=2?
Since xy > 0, we know that x≠0.
Thus, the resulting question is as follows:
Does x=2?

Since the only constraint in statement 2 is that x=y, x can be equal to ANY VALUE.
Thus, we cannot determine whether x=2.
INSUFFICIENT.
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by psm12se » Sat Feb 08, 2014 12:16 am
Thanks all for the replies. Got it now.
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