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Algebra

by mehulv » Mon Jun 21, 2010 8:05 am
Given that A = 3y + 8x, B = 3y - 8x, C = 4y + 6x, and D = 4y - 6x, what is the value of x*y?

1. AB + CD = -275
2. AD - BC = 420
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by gmatmachoman » Mon Jun 21, 2010 9:26 am
mehulv wrote:Given that A = 3y + 8x, B = 3y - 8x, C = 4y + 6x, and D = 4y - 6x, what is the value of x*y?

1. AB + CD = -275
2. AD - BC = 420
Its a bit lengthy calculative one..still it may pop up !!

Pick B

st 1:
apply those values of A,B,C,D

we will get y^2 - 4X^2 = -11

x*y can take any number of values .Insufficient

st 2


apply those values of A,B,C,D

we will get 28 X*Y = 420

X*Y =15

Pick B..Move on!!
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by tpr-becky » Mon Jun 21, 2010 11:57 am
this is a quadratics problem - you have to solve each of the quadratics using FOIL and then see how they relate to each other, a calculation intensive problem but certainly doable if you recognize the method from the begining.
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by gmatmachoman » Tue Jun 22, 2010 1:01 am
tpr-becky wrote:this is a quadratics problem - you have to solve each of the quadratics using FOIL and then see how they relate to each other, a calculation intensive problem but certainly doable if you recognize the method from the begining.
@becky--- My query is will these sort of questions pop up in real test???What I see, is every problem has some logic/hidden fundae which we are forced to unplug.

Whereas in calculative ones, I don't think we apply logic..so what are the chances???
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by tpr-becky » Tue Jun 22, 2010 6:53 am
This question is plausible - it isn't the normal type of question we have been seeing but the GMAT seems to be shifting to include more problems that you actually have to calculate - although most of these have been in the inequalities. You still don't have to solve the entire thing until you get to teh end of B becuase it is clear that statemetn 1 will get you two squares by looking at the law of quadratics (x-y)(x+y)=x^2 - y^2. This problem is good to study becuase it helps with the Quadratic reasoning.
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by outreach » Tue Jun 22, 2010 11:42 am
B

option1

AB = (3y + 8x)(3y - 8x) = 9y2 - 64x2
CD = (4y + 6x)(4y - 6x) = 16y2 - 36x2
AB + CD = 25y2 - 100x2
AB + CD = 25(y2 - 4x2)
AB + CD = 25(y + 2x)(y - 2x)

now given AB + CD = -275
hence
-275= 25(y + 2x)(y - 2x)
-11=(y + 2x)(y - 2x)
now
(y + 2x)=-11 or (y - 2x)=-11
Y=+1,X=-6 OR Y=1,X=5
INSUFFICIENT

option2
AD = (3y + 8x)(4y - 6x) = 12y2 + 14xy - 48x2
BC = (3y - 8x)(4y + 6x) = 12y2 - 14xy - 48x2
AD - BC = 14xy - (-14xy) = 28xy

given AD - BC = 420
hence
420=28xy
xy=15
suff
mehulv wrote:Given that A = 3y + 8x, B = 3y - 8x, C = 4y + 6x, and D = 4y - 6x, what is the value of x*y?

1. AB + CD = -275
2. AD - BC = 420
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