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# Given that x and y are real numbers, what is the value of x

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Intern
Joined: 15 Sep 2007
Posts: 26
Given that x and y are real numbers, what is the value of x  [#permalink]

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23 Sep 2007, 09:00
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Given that x and y are real numbers, what is the value of x + y ?

1) (x² – y²) / (x-y) = 7
2) (x + y)² = 49

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Manager
Status: Post MBA, working in the area of Development Finance
Joined: 09 Oct 2006
Posts: 153
Location: Africa

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23 Sep 2007, 09:15
A.
St. 1 (x² – y²) / (x-y) = 7 =>x+y = 7 - suff
st. 2 x+y = +7 - insuff
VP
Joined: 08 Jun 2005
Posts: 1109

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23 Sep 2007, 09:20
x+y = ?

statement 1

(x^2-y^2)/(x-y) = 7

(x+y)(x-y)/(x-y) = 7

x+y = 7

sufficient

statement 2

(x+y)^2 = 49

(x+y) = 7 or -7

insufficient

agree with Artemov (A)

Intern
Joined: 15 Sep 2007
Posts: 26

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23 Sep 2007, 11:48
In statetement (1), how can you cancel (x-y) from numerator and denominator..what if x=y ? The question never says that x can't be equal to y. Any thoughts ?
VP
Joined: 08 Jun 2005
Posts: 1109

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23 Sep 2007, 11:57
coldweather999 wrote:
In statetement (1), how can you cancel (x-y) from numerator and denominator..what if x=y ? The question never says that x can't be equal to y. Any thoughts ?

If x=y then I think that the expression (x^2-y^2)/(x-y) = 7 could never equal 7, could it ?

Manager
Joined: 29 Jul 2007
Posts: 177

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23 Sep 2007, 14:19

I think everyone agrees that Statement I is sufficient.

But isn't Statement II sufficient as well? I was always told that in Gmat Math, square root of a number is only the positive root (i.e. 49^(1/2) = 7 only, not -7).

Any thoughts? Whats the OA?
Intern
Joined: 21 Jul 2005
Posts: 1

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23 Sep 2007, 19:44
I too initially had the same thoughts, but on rethinking as to what GMAT Math actually says, I figured it should be +7 and -7(and not just+7) . Here was what I interpreted.
Gmat Math tells the sqaure root of any given no is represted by n^(1/2) and n^-(1/2).It actually means that n^(1/2) represents only the positive sq root of n and n^-(1/2) the negative sq root. Had the question asked for n^(1/2) then it would have been only the postive sqaure root.But here it asks indirectly to find the numbers whose sqaures equal 49 - which happens to be 49^(1/2) and 49^-(1/2) (i.e +7 and -7). Hope I have got this right and you are clear with the explanation.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4759
Location: Singapore

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23 Sep 2007, 20:14
St1:
x+y = 7 --> sufficient.

St2:
(x+y)^2 - 7^2 = 0
((x+y)+7)((x+y)-7) = 0

x+y = 7, x+y = -7
Insufficient

Ans A
Manager
Joined: 29 Jul 2007
Posts: 177

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23 Sep 2007, 20:30
I don't mean to belabor this point, but here is an excerpt from Veritas's Algebra Notes regarding sq roots:
"For even roots of all positive numbers, there are two solutions - one positive and one negative. However, when the radical sign is used, the question is only asking for the principal square root"
example
sq root of 16 = +4 only.

So am not sure why the answer is A? Is it A b/c the "radical sign" is not explicitly used in the problem?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4759
Location: Singapore

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23 Sep 2007, 20:34
Skewed wrote:
I don't mean to belabor this point, but here is an excerpt from Veritas's Algebra Notes regarding sq roots:
"For even roots of all positive numbers, there are two solutions - one positive and one negative. However, when the radical sign is used, the question is only asking for the principal square root"
example
sq root of 16 = +4 only.

So am not sure why the answer is A? Is it A b/c the "radical sign" is not explicitly used in the problem?

my understanding of that statement given by verita is:

If we are sayign x^2 = 4--> there are two solutions. x = 2, x = -2.
If we are saying sqrt(4), there is only one solution, that is 2.

It is A becsause the numerator is in the form a^2-b^2 which we can expand to (a+b)(a-b). We can cancel out the term in the denominator leaving us with jsut a+b. That's why it is sufficient for A. Nothing to do with radicals.
Manager
Joined: 29 Jul 2007
Posts: 177

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23 Sep 2007, 21:19
ywilfred,

Thanks 4 the reply. My contention was not so much for why Statement I is correct, but why Statement II is incorrect given the foregoing sq root concern. But if you're saying its A, i'll assume its correct.
VP
Joined: 10 Jun 2007
Posts: 1340

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23 Sep 2007, 21:46
Skewed wrote:

I think everyone agrees that Statement I is sufficient.

But isn't Statement II sufficient as well? I was always told that in Gmat Math, square root of a number is only the positive root (i.e. 49^(1/2) = 7 only, not -7).

Any thoughts? Whats the OA?

II is not sufficient
In GMAT, if you are given:
x^2 = 49, the answer is +/- 7
If you are given:
x = sqrt(49), the answer is 7
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Re: Given that x and y are real numbers, what is the value of x  [#permalink]

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08 Jan 2018, 21:20
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--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Given that x and y are real numbers, what is the value of x   [#permalink] 08 Jan 2018, 21:20
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