Author 
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furtadovinod

Post subject: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Thu Jul 23, 2009 11:27 am 


Students 

Posts: 28

Hi,
A minor issue in the answer explanation to this problem. I am not copying out the entire explanation.
If x and y are integers such that x < y < 0, what is x â€“ y?
(1) (x + y)(x â€“ y) = 5 (2) xy = 6
Part of the explanation given is
As you can see, the difference between squares grows as the squares themselves get larger. The only difference between two squares that equals 5 is the difference between 4 and 9. Since x and y are both negative, this tells us that x = 3 and y = 2; therefore, x â€“ y = 5.
The bolded portion should be x  y = (3)  (2) = (3) + 2 = 1





www.mbachase.com

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Fri Jul 24, 2009 1:27 am 


Forum Guests 

Posts: 12

[Attention mbachase.com: we appreciate your desire to help GMAT students. Unfortunately, we don't host posts from competitors on our forums. If you'd like to offer free services to your students (and I think that's a great idea!), then you might consider starting your own forums. Good luck! Stacey]
Last edited by www.mbachase.com on Thu Aug 20, 2009 12:36 am, edited 1 time in total.





Ben Ku

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Tue Aug 18, 2009 1:23 pm 


ManhattanGMAT Staff 

Posts: 818

Hi furtadovinod,
Thanks for the correction. I'll be sure to forward this to the right people so that it gets corrected on our explanations.
_________________ Ben Ku Instructor ManhattanGMAT





heydharini

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Tue Oct 13, 2009 2:13 am 


Students 

Posts: 3

Hi,
I came across the same question in my Manhattan test today and I felt that the answer could be D
If x and y are integers such that x < y < 0, what is x â€“ y?
(1) (x + y)(x â€“ y) = 5 (2) xy = 6
Considering B alone here, [according to this question A is the answer and the explanation is provided  only correction needed x  y = 1]
xy = 6 The options here are 3 and 2 Since we know x<y<0 , x= 3 and y=2
x  y = 3  (2) = 1
which means D should be the correct answer. Manhattan Staff, please let me know if am right?
Thanks,





mkorrapati

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Wed Oct 21, 2009 10:57 am 


Students 

Posts: 2

Hey heydharini,
What about x = 6 and y = 1?
This makes xy = 6 as well.
Now you have two different solutions for xy. So B and D can not be the answers.





RonPurewal

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Mon Nov 02, 2009 10:23 pm 


ManhattanGMAT Staff 

Posts: 11197

mkorrapati wrote: Hey heydharini,
What about x = 6 and y = 1?
This makes xy = 6 as well.
Now you have two different solutions for xy. So B and D can not be the answers. correct.
_________________ Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi
Un bon vÃªtement, c'est un passeport pour le bonheur. Yves SaintLaurent





lancequas

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Tue May 25, 2010 11:32 pm 


Students 

Posts: 3

I got the answer right by accident I guess; I surmized that x^2y^2 =5 thus xy= +/ sq. root 5. Knowing x and y are both negative and x is farther away from zero xy must = neg. sq. root 5. I'm still not seeing why this is wrong. Please correct me and explain the answer





adiagr

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Sun Jun 06, 2010 3:09 pm 


Students 

Posts: 88

The term is [(x^2)  (y^2)] and not (xy)^2.
You cannot take square root for the left hand side i.e. for
[(x^2)  (y^2)].
I hope that helps.
Aditya.





RonPurewal

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Wed Jun 23, 2010 9:30 am 


ManhattanGMAT Staff 

Posts: 11197

adiagr wrote: The term is [(x^2)  (y^2)] and not (xy)^2.
You cannot take square root for the left hand side i.e. for
[(x^2)  (y^2)].
I hope that helps.
Aditya. yes. this confusion is going to be a very bad thing on the test, if it persists. therefore, you should probably pick up an algebra book  or surf the internet  and look up "difference of squares" and "perfect square trinomials"; these are the two factoring patterns that you are confusing. you may also want to check out the uses of the distributive property; you are mistakenly applying it to square roots, when in fact it only applies to multiplication and division.
_________________ Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi
Un bon vÃªtement, c'est un passeport pour le bonheur. Yves SaintLaurent





yousuf_azim

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Mon Sep 05, 2011 1:38 am 


Students 

Posts: 47





jnelson0612

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Sat Oct 15, 2011 10:40 pm 


ManhattanGMAT Staff 

Posts: 2574

yousuf_azim wrote: What is the ans?
BR The answer is A.
_________________ Jamie Nelson ManhattanGMAT Instructor





HIK

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Fri Nov 11, 2011 9:23 am 


Students 

Posts: 1

Hi Guys,
Is there any way of finding out a solution algebrically?
During the exam testing numbers, always makes one wonder if there may be more solutions?
I understand that x and y are integers so the options for testing numbers is less, but still if there is an algebric solution, it'll be great.
Thanks, Hassan





tim

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Fri Nov 25, 2011 1:35 pm 


ManhattanGMAT Staff 

Posts: 4758 Location: Southwest Airlines, seat 21C

Hassan, if you are interested in a solution that uses more algebra than what you've already seen in the posts above, that is probably not a good idea. The fact that x and y are integers means that you should factor that into your solution method in order to make things easier. A purely algebraic solution that only restricts x and y to integers at the end would be much less efficient..
_________________ Tim Sanders Manhattan GMAT Instructor





chughbrajesh

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Wed Jan 29, 2014 3:32 am 


Course Students 

Posts: 22

(xy)(x+y)=5
We need to figure out the value for xy. Couldn't xy= 1 or 5? So we are not sure about the (xy) value?
Also if x is smaller than y and y is smaller than 0 then it means that x must be 4 and y must be 1 to make (xy)=5. The question says "x < y < 0". Then (x+y) will not equal 1 to make a positive 5. This will not happen because one 4 and other is 1. no way, it will equal 1.





RonPurewal

Post subject: Re: If x and y are integers such that x < y < 0, what is x â€“ y? Posted: Wed Jan 29, 2014 10:32 am 


ManhattanGMAT Staff 

Posts: 11197

chughbrajesh wrote: (xy)(x+y)=5
We need to figure out the value for xy. Couldn't xy= 1 or 5? So we are not sure about the (xy) value?
Also if x is smaller than y and y is smaller than 0 then it means that x must be 4 and y must be 1 to make (xy)=5. The question says "x < y < 0". Then (x+y) will not equal 1 to make a positive 5. This will not happen because one 4 and other is 1. no way, it will equal 1. You're correct that x  y doesn't equal 5. Both numbers are negative, so x + y will be more negative (= farther to the left on the number line) than x  y. Since everything is in terms of integers, that leaves only one possibility: x  y = 1 and x + y = 5. So, sufficient. (You'll get x = 3 and y = 2, although, as long as you know it guarantees a unique answer, it's unnecessary to solve the system once you've found it).
_________________ Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi
Un bon vÃªtement, c'est un passeport pour le bonheur. Yves SaintLaurent





