gmat prep problem

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olika: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sat Nov 10, 2007 10:35 am; Thanked: 1 times

by olika » Mon Jun 23, 2008 7:47 am

Hi everybody!
Here is a problem from GMAT prep:
if xy=1, what is the value of (2*(x+y)^2)/(2*(x-y)^2)?

answer choice:
1) 2
2) 4
3) 8
4) 16
5) 32

I know the right answer, but it's interesting to know how to solve this problem

p.s.: The same quest. already was posted by another user here: https://www.beatthegmat.com/if-xy-1-t12255.html, but nobody has given the answer.

Thank you in advance!

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Source: Beat The GMAT — Problem Solving | Mon Jun 23, 2008 7:47 am

atlantic: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Apr 27, 2008 10:31 am; Location: Portugal; Thanked: 7 times

by atlantic » Mon Jun 23, 2008 8:13 am

Hi Olika,

I think the question is not correctly posted.

Should be: Is if xy=1 what is the value of (2^(x+y)^2)/(2^(x-y)^2)?

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

=(2^x^2*2^2xy*2^y^2)/(2^x^2*2^-2xy*2^y^2)

=(2^2xy)/(2^-2xy)

=(2^2xy)*(2^2xy), as xy=1, =2^2*2^2=8

Let me know you miss something.

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sethids: Master | Next Rank: 500 Posts; Posts: 135; Joined: Mon Jun 23, 2008 3:56 am; Thanked: 7 times

Answer is D

by sethids » Mon Jun 23, 2008 8:25 am

I agree with Atlantic but for his final calculation.
In the last step 2^2*2^2=16 and not 8... hence D is the answer.

I have no clue if the question originally posted (by olika) was correct. Would be curious to know the approach in that case.

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spanlength: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sat Mar 15, 2008 10:54 pm

by spanlength » Mon Jun 23, 2008 8:25 am

i agree with atlantic about the posting of the question.
But the answer is 16.In the last line atlantic has written 8 instead of 16.
Also we know that
(x+y)^2 - (x-y)^2 = 4xy
So we can directly write
[2^((x+y)^2)]/[2^((x-y)^2)]
= 2^[(x+y)^2 - (x-y)^2] = 2^4xy = 2^4 = 16 (since xy= 1).

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atlantic: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Apr 27, 2008 10:31 am; Location: Portugal; Thanked: 7 times

by atlantic » Mon Jun 23, 2008 8:32 am

Thanks guys,

Of course 2^2*2^2=16 and not 8 as I wrote.

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olika: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sat Nov 10, 2007 10:35 am; Thanked: 1 times

by olika » Mon Jun 23, 2008 8:38 am

atlantic wrote:Hi Olika,

I think the question is not correctly posted.

Hi Atlantic,

The question that i've posted is correct

Here is the screen shot

Attachments

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Mon Jun 23, 2008 9:09 am

This question has been discussed several times. There is a typo in the question. It's supposed to include unknown exponents as is mentioned above.

https://second-lap.blocked/

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atlantic: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Apr 27, 2008 10:31 am; Location: Portugal; Thanked: 7 times

by atlantic » Mon Jun 23, 2008 9:32 am

Thanks aleksandrM,

You juts saved me from madness as I was trying to solve the problem as seen on the screen shot. LOL

But please tell me: how can the GMAT has typos? Is it possible? Has this happened before? Can we find things like this on real GMAT, wasting our precious time on a typo?

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Mon Jun 23, 2008 9:41 am

While GMATPrep has a number of typos, I would say that it is highly unlikely that you will find typos on the real test. However, if you are not satisfied with your score on the real exam, you can appeal.

https://second-lap.blocked/

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olika: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sat Nov 10, 2007 10:35 am; Thanked: 1 times

by olika » Mon Jun 23, 2008 11:21 am

AleksandrM wrote:This question has been discussed several times. There is a typo in the question. It's supposed to include unknown exponents as is mentioned above.

It's awful that they do mistakes in preparation materials. I agree with Atlantic.
Anyway, thank you. It's good to know that it is somebody's mistake rather than my dullness

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