Mar 18 10:00 PM AKDT  11:00 PM AKDT Getting 700+ on the GMAT isn’t about luck. It’s about taking action and start preparing early. Start studying today with 20% off on your GMAT prep. Mar 19 08:00 AM PDT  09:00 AM PDT Beat the GMAT with a customized study plan based on your needs! Learn how to create your preparation timeline, what makes a good study plan and which tools you need to use to build the perfect plan. Register today! Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
Intern
Joined: 15 Sep 2007
Posts: 26

Given that x and y are real numbers, what is the value of x
[#permalink]
Show Tags
23 Sep 2007, 09:00
Question Stats:
100% (00:00) correct 0% (00:00) wrong based on 7 sessions
HideShow timer Statistics
Given that x and y are real numbers, what is the value of x + y ?
1) (x² – y²) / (xy) = 7
2) (x + y)² = 49 == 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 repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



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

A.
St. 1 (x² – y²) / (xy) = 7 =>x+y = 7  suff
st. 2 x+y = +7  insuff



VP
Joined: 08 Jun 2005
Posts: 1109

x+y = ?
statement 1
(x^2y^2)/(xy) = 7
(x+y)(xy)/(xy) = 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

In statetement (1), how can you cancel (xy) 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

coldweather999 wrote: In statetement (1), how can you cancel (xy) 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^2y^2)/(xy) = 7 could never equal 7, could it ?



Manager
Joined: 29 Jul 2007
Posts: 177

Isn't the answer D?
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

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

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

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

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^2b^2 which we can expand to (a+b)(ab). 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

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

Skewed wrote: Isn't the answer D?
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



NonHuman User
Joined: 09 Sep 2013
Posts: 10129

Re: Given that x and y are real numbers, what is the value of x
[#permalink]
Show Tags
08 Jan 2018, 21:20
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. == 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 repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




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






