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.
DS:Inequalities
This topic has expert replies
GMAT/MBA Expert
- Mike@Magoosh
- GMAT Instructor
- Posts: 768
- Joined: Wed Dec 28, 2011 4:18 pm
- Location: Berkeley, CA
- Thanked: 387 times
- Followed by:140 members
Dear psm12se,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.
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/
https://gmat.magoosh.com/
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The portion in red misrepresents the problem.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.
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3