xy=1

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Sat Jan 03, 2009 7:14 pm

if xy=1, what is the value of [2(x+y)^2]/[2(x-y)^2]?

2
4
8
16
32

OA is 16

I tried to plug in numbers but that doesn't work

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Source: Beat The GMAT — Problem Solving | Sat Jan 03, 2009 7:14 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Jan 03, 2009 7:18 pm

Question should read(I think its been posted before)

2^(x+y)^2 / 2^(x-y)^2

2 ^ (x^2+y^2+2xy) / 2^(x^+y^2-2xy) (a^m / a^n = a^(m-n))

2 ^(x^2+y^2+2xy-x^2-y^2+2xy)

2^(4xy)

2^4

16

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Sat Jan 03, 2009 7:26 pm

this is the original question captured img

Attachments

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Sat Jan 03, 2009 7:28 pm

could that be a type error from the prep software?

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sat Jan 03, 2009 7:29 pm

so plugging numbers are useful in these question types in which you have no limitations for your X and Y

XY=1 means : X=1 and Y=1

So , the question turns into 2^4/1 = 16

That's it!

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 03, 2009 7:52 pm

Hmm, the question as it stands couldn't be a GMAT question.
To begin, there would have been a proviso that rules out the possibility of the denominator = 0 (e.g., x cannot equal y)
Also, the value of this rational expression varies as we plug in different values for x and y such that xy=1.
Where did you find this question?

Brent Hanneson - Creator of GMATPrepNow.com

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Jan 03, 2009 8:00 pm

XY=1 means : X=1 and Y=1

x=-1 y=-1 also possible(in general) but I guess it doesnt make a difference for this problem

x=2 y=1/2

x=3 y=1/3

....... So on

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sat Jan 03, 2009 8:10 pm

Brent Hanneson wrote:Hmm, the question as it stands couldn't be a GMAT question.
To begin, there would have been a proviso that rules out the possibility of the denominator = 0 (e.g., x cannot equal y)
Also, the value of this rational expression varies as we plug in different values for x and y such that xy=1.
Where did you find this question?

X can be equal to Y and this gives us 2^0=1

Cramya,

How about 4 x 1/4

X=Y=1 is an example that requires the less work.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Sat Jan 03, 2009 8:32 pm

Brent Hanneson wrote:Hmm, the question as it stands couldn't be a GMAT question.
To begin, there would have been a proviso that rules out the possibility of the denominator = 0 (e.g., x cannot equal y)
Also, the value of this rational expression varies as we plug in different values for x and y such that xy=1.
Where did you find this question?

I found this on the OG prep software, its in CAT 1. This is prob not the latest version because I am using my old computer and I installed the gmat prep on this computer quite a while ago.

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rajataga: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Tue Dec 23, 2008 11:06 pm; Thanked: 2 times

by rajataga » Sun Jan 04, 2009 2:55 am

logitech wrote:
Brent Hanneson wrote:Hmm, the question as it stands couldn't be a GMAT question.
To begin, there would have been a proviso that rules out the possibility of the denominator = 0 (e.g., x cannot equal y)
Also, the value of this rational expression varies as we plug in different values for x and y such that xy=1.
Where did you find this question?
X can be equal to Y and this gives us 2^0=1

Cramya,

How about 4 x 1/4

X=Y=1 is an example that requires the less work.

The denominator would be 0 if the X and Y are equal, since it's not 2^0, but 2 X 0....

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sun Jan 04, 2009 11:26 am

rajataga wrote:

The denominator would be 0 if the X and Y are equal, since it's not 2^0, but 2 X 0....

My poor old eyes

Thanks!

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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