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freyesinsb: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Thu Aug 25, 2011 2:13 pm

GMATAdvanced GMAT Math Question

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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Source: Beat The GMAT — Data Sufficiency | Wed Feb 06, 2013 10:25 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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freyesinsb: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Thu Aug 25, 2011 2:13 pm

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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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

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:
( 2xÂ²(x+3)-2x-6 ) / (xÂ²+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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