If x+2y=a , and x-2y=b, which of the following is an expression for xy?
A)2(a+b/a-b)
b)2(a-b/a+b)
c)1
d)non
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abhijit@prepitt
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Need to point out that usually there are 5 choices in the test. None is usually (E). Also double check if the question asks xy or x/y.Hmna wrote:If x+2y=a , and x-2y=b, which of the following is an expression for xy?
A)2(a+b/a-b)
b)2(a-b/a+b)
c)1
d)non
x+2y = a
x-2y = b
Add equations:
==> x=(a+b)/2
Subtract equations
==> y = (a-b)/4
xy = (a^2-b^2)/8
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Brent@GMATPrepNow
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A quick approach is to PLUG IN SOME VALUESHmna wrote:If x+2y=a , and x-2y=b, which of the following is an expression for xy?
A)2(a+b/a-b)
b)2(a-b/a+b)
c)1
d)non
let x = 0 and let y = 0
This means that a = 0 and b = 0
We want to find the value of xy
Since x = 0 and y = 0, xy = (0)(0) = 0
Now we'll check the answer choices to see which one equals 0, when we plug in a = 0 and b = 0
A)2(a+b/a-b) = 2(0+0/(0-0) = 0/0 = undefined. Does not equal 0, ELIMINATE
B)2(a-b/a+b) = 2(0-0/(0+0) = 0/0 = undefined. Does not equal 0, ELIMINATE
C)1 Does not equal color=red]0[/color], ELIMINATE
By the process of elimination, the correct answer must be D
Cheers,
Brent
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Matt@VeritasPrep
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Since we've got
x + 2y = a
x - 2y = b
we know that a = b + 4y, or a - b = 4y
Likewise, adding the two equations together, we know that a + b = (x + 2y) + (x - 2y) = 2x
So we can now replace (a + b) with 2x and (a - b) with 4y.
Working with the answers, this gives us:
(A) 2 * (a + b)/(a - b) => 2 * 2x/4y => 4x/4y = x/y
Not right!
How about (B)?
2 * (a - b)/(a + b) => 2 * 4y / 2x => 4y/x
Nope!
(C) would work if y = 1/x, but we saw above that that isn't the case.
From there, we're left with the disappointing (D).
x + 2y = a
x - 2y = b
we know that a = b + 4y, or a - b = 4y
Likewise, adding the two equations together, we know that a + b = (x + 2y) + (x - 2y) = 2x
So we can now replace (a + b) with 2x and (a - b) with 4y.
Working with the answers, this gives us:
(A) 2 * (a + b)/(a - b) => 2 * 2x/4y => 4x/4y = x/y
Not right!
How about (B)?
2 * (a - b)/(a + b) => 2 * 4y / 2x => 4y/x
Nope!
(C) would work if y = 1/x, but we saw above that that isn't the case.
From there, we're left with the disappointing (D).
