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If x+y=a and x-y=b, then 2xy=? a) (a^2 - b^2)/2 b)

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Intern
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If x+y=a and x-y=b, then 2xy=? a) (a^2 - b^2)/2 b)  [#permalink]

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New post 27 Jan 2005, 21:47
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

86% (01:26) correct 14% (00:00) wrong based on 42 sessions

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:twisted:

14. If x+y=a and x-y=b, then 2xy=?

a) (a^2 - b^2)/2

b) (b^2 - a^2)/2

c) (a - b )/2
d) (ab)/2
e) (a^2 + b^2)/2

There must be a FAST way to do this. Pluggin' in takes too long.

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Intern
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New post 27 Jan 2005, 22:06
1
Square both the sides and then substract

(x + y)^2 = a^2
- (x - y)^2 = b^2

4xy = a^2 - b^2
2xy = a^2 - b^2/2
Director
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New post 28 Jan 2005, 05:13
when u see these kind of formula just do algeraic maniuplation not plug in tht will work fast
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New post 28 Jan 2005, 07:37
Just notice that you need a positive product "2xy" so the sign before b whatever the power must be negative : this reduces the choice between A and C.

Then between A and C you need a power to have square terms (a-b does not lead in any way to xy...)

So answer is A

In this way it takes no more than 20 sec.
Manager
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New post 28 Jan 2005, 08:03
Great tip twixt. I would not have thought about going this way. I went about solving it. Even that took around 30-40 sec...... But good tip.
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New post 28 Jan 2005, 13:26
:evil: thanks to you all!
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New post 30 Jan 2005, 07:27
excellent tip. I think the hard part for most of us is keeping our cool when hit with such questions, and trying to understand what is going in instead of jumping into the calculations. Any tips on how to overcome these?
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Agree with Keeping Cool  [#permalink]

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New post 01 Feb 2005, 10:42
My biggest problems are often these types of questions. i see them and my mind freaks out.

I have learned that often they want you to square it first or multiply by 1 in the form of x^2y/y or something.

Those are my two cents but i could use some advice myself.
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New post 01 Feb 2005, 18:19
my tip ?

not to crack the formula as it ll take tremendous time.
here : Narrow the possible solutions then replace
c & d, definitively not
e, tougher but also obvious

we are left with
a or b

plug the assumptions and simplify.
you got it ! A

--== Message from the GMAT Club Team ==--

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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: If x+y=a and x-y=b, then 2xy=? a) (a^2 - b^2)/2 b)  [#permalink]

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New post 27 Dec 2018, 10:07
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Re: If x+y=a and x-y=b, then 2xy=? a) (a^2 - b^2)/2 b)   [#permalink] 27 Dec 2018, 10:07
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