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Source: — Data Sufficiency |
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by MartyMurray » Sun Oct 25, 2015 7:43 am
Having to do any algebra is annoying to me sometimes, but I guess I will bang this one out.

(1) (x + y)(1/x + 1/y) = 16

Multiply out the left side to get 1 + y/x + x/y + 1 = 16

y/x + x/y = 14

If x were equal to y, then y/x and x/y would both be 1. So y/x + x/y would be 2, instead of 14.

So x does not equal y and Statement 1 is sufficient.

Hmm. That wasn't too annoying. Maybe I should lighten up.

Taking Statement 2, (x - 3)2 - (y - 3)2 = 0, we can divide the entire thing by 2 and get (x - 3) - (y - 3) = 0.

This becomes (x - 3) = (y - 3), and so obviously x = y and Statement 2 is sufficient as well.

There is an issue with this question as the two statements give different answers to the question, which situation does not make sense. Official GMAT questions are set up so that the statements and any data given in the question are consistent.

Still, I guess one can go with it and choose D.
Last edited by MartyMurray on Sun Oct 25, 2015 12:41 pm, edited 2 times in total.
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by theCEO » Sun Oct 25, 2015 7:58 am
Marty Murray wrote:
Taking Statement 2, (x - 3)2 - (y - 3)2 = 0, we can multiply the entire thing by 2 and get (x - 3) - (y - 3) = 0.
Hi Marty,

Could you verify the above calculation please?
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by MartyMurray » Sun Oct 25, 2015 12:44 pm
Fixed it. I guess that's why you're management!!!
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by Matt@VeritasPrep » Sun Oct 25, 2015 11:11 pm
S1::

Suppose x = y. Then we have

(x + x)(1/x + 1/x) = 16, or

(2x)(2/x) = 16, or

4 = 16. This is preposterous, so x ≠ y; SUFFICIENT.

S2::

(x - 3)² - (y - 3)² = 0

(x - 3)² = (y - 3)²

So y = x or y = 6 - x; NOT SUFFICIENT.

The answer is A.
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by Matt@VeritasPrep » Sun Oct 25, 2015 11:14 pm
Marty Murray wrote:There is an issue with this question as the two statements give different answers to the question, which situation does not make sense. Official GMAT questions are set up so that the statements and any data given in the question are consistent.
This is an issue with several of the questions this user has posted, but as far as I can tell this question is actually fine. (I'm guessing S2 is (x - 3)² = (y - 3)², not 2*(x - 3) = 2*(y - 3); virtually any time I see x2 on this forum, the poster seems to mean to have typed x².)
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by theCEO » Mon Oct 26, 2015 2:41 am
Marty Murray wrote:Fixed it. I guess that's why you're management!!!
Haha! Actually I thought there was a typo with this statement: (x - 3)2 - (y-3)2 = 0.
I always see similar statements written as 2(x - 3) - 2(y-3) = 0 if the terms were to be multiplied together. I thought the poster meant (^2) instead.
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by oquiella » Tue Oct 27, 2015 2:25 pm
theCEO wrote:
Marty Murray wrote:Fixed it. I guess that's why you're management!!!
Haha! Actually I thought there was a typo with this statement: (x - 3)2 - (y-3)2 = 0.
I always see similar statements written as 2(x - 3) - 2(y-3) = 0 if the terms were to be multiplied together. I thought the poster meant (^2) instead.
Sorry. Yes i meant (^2)
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by Matt@VeritasPrep » Fri Oct 30, 2015 12:32 am
oquiella wrote:
theCEO wrote:
Marty Murray wrote:Fixed it. I guess that's why you're management!!!
Haha! Actually I thought there was a typo with this statement: (x - 3)2 - (y-3)2 = 0.
I always see similar statements written as 2(x - 3) - 2(y-3) = 0 if the terms were to be multiplied together. I thought the poster meant (^2) instead.
Sorry. Yes i meant (^2)
You can always use superscripts: just copy and paste, or use the shortcut code. (The superscripts are so much easier to read; most of the experts use them on the forums for that reason.)
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