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help !!

by Hmna » Tue May 09, 2017 4:12 am
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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by abhijit@prepitt » Thu May 11, 2017 10:46 am
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
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.


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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by Brent@GMATPrepNow » Thu May 11, 2017 12:19 pm
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
A quick approach is to PLUG IN SOME VALUES

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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by Matt@VeritasPrep » Thu May 11, 2017 8:29 pm
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).
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