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by freyesinsb » Wed Feb 06, 2013 10:25 am
This is a problem from the readyforGMAT.COM advanced math section. I can't seem to figure out an easy way to tackle it. Please advise. Thanks.


Which of the following is equivalent to 2x^2(x+3)-2x-6/x^2+2x-3 for all values of x for which both expressions are defined?

A.2x^2-2

B.2x+2

C.x+1

D.2x+6

E.x-1
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by Brent@GMATPrepNow » Wed Feb 06, 2013 10:39 am
freyesinsb wrote:This is a problem from the readyforGMAT.COM advanced math section. I can't seem to figure out an easy way to tackle it. Please advise. Thanks.


Which of the following is equivalent to 2x^2(x+3)-2x-6/x^2+2x-3 for all values of x for which both expressions are defined?

A.2x^2-2

B.2x+2

C.x+1

D.2x+6

E.x-1
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Answer = B

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by freyesinsb » Wed Feb 06, 2013 11:02 am
Hi Brent, thanks for the reply. I know the answer but I'm looking for an easy/less time consuming way to solve this problem/similar problems.
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by Brent@GMATPrepNow » Wed Feb 06, 2013 11:14 am
You can also try plugging in values, but this is not always faster (it is here, though).

For example, if x=0, then we can evaluate our expression by plugging in 0 to get:
[2((0)^2)(0+3) - 2(0) - 6]/[0^2 + 2(0) - 3]
= (-6)/(-3)
= 2

So, when x=0, our expression evaluates to be 2

For an answer choice to be equivalent to the given expression, it too must evaluate to be 2.

A. 2x^2-2 = 2(0)^2 - 2 = -2 (no good - eliminate it)

B.2x+2 = 2(0) + 2 = 2 (nice - keep it)

C.x+1 = 0 + 1 = 1 (no good - eliminate it)

D.2x+6 = 2(0) + 6 = 6 (no good - eliminate it)

E.x-1 = 0 - 1 = -1 (no good - eliminate it)

So, the answer = B

Cheers,
Brent
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by GMATGuruNY » Wed Feb 06, 2013 12:05 pm
freyesinsb wrote:This is a problem from the readyforGMAT.COM advanced math section. I can't seem to figure out an easy way to tackle it. Please advise. Thanks.


Which of the following is equivalent to 2x^2(x+3)-2x-6/x^2+2x-3 for all values of x for which both expressions are defined?

A.2x^2-2

B.2x+2

C.x+1

D.2x+6

E.x-1
Let x=0.
Then:
( 2x²(x+3)-2x-6 ) / (x²+2x-3) = -6/-3 = 2. This is our target.

Now we plug x=0 into the answer choices to see which yields our target of 2.
Only B works:
2x+2 = 2*0 + 2 = 2.

The correct answer is B.
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by freyesinsb » Wed Feb 06, 2013 2:54 pm
Thanks!
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