BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Quadratic Equation Problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sat Jun 23, 2012 11:16 am

Quadratic Equation Problem

by [email protected] » Tue Jan 01, 2013 11:08 am
If \frac{3}{x+3}+\frac{4}{x+4}=\frac{2}{x+2}+\frac{5}{x+5}, then the value of x is



A. \frac {13}{4}


B. -\frac {5}{2}


C. -\frac {7}{2}


D. \frac {9}{2}


E. \frac {17}{2}

Can someone kindly help me in answering this question. The source of this question is Jumbo Tests.

Thanks in advance.
SD
Top
Source: — Quantitative Reasoning |
User avatar
MBA Admissions Consultant
Posts: 2279
Joined: Fri Nov 11, 2011 7:51 am
Location: New York
Thanked: 660 times
Followed by:266 members
GMAT Score:770

by Jim@StratusPrep » Wed Jan 09, 2013 6:50 am
It is a little hard to understand the notations. Can you rewrite or potentially use an image?
GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review

Image
Top
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Sun Dec 19, 2010 1:49 pm
Thanked: 11 times
Followed by:2 members

by jitsy » Fri Jul 19, 2013 7:15 am
Could anyone solve this ques. The only thing I can figure out is that in the ques itself, in a way, 3 and 4 have been written as 2+1 and 5-1 which becomes 2+5 (if you know what I mean). Experts?
If you appreciated my post or even just my time trying to help, please don't forget to click on 'Thanks' and say "Piece o' Cake mate" at the same time.
Top
User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Jul 19, 2013 5:25 pm
Hi everyone,

I think that the question is supposed to be this:

3/(x+3) + 4/(x+4) = 2/(x+2) + 5/(x+5) x = ?

13/4
-5/2
-7/2
9/2
17/2

I've come to a solution by using the following math steps:

First, set a common denominator for the left and a separate common denominator for the right. You'll notice an interesting PATTERN.

3(x+4) + 4(x+3) 2(x+5) + 5(x+2)
------------- = ----------------
(x+3)(x+4) (x+2)(x+5)


7x + 24 7x + 20
------------- = --------------
x^2 + 7x + 12 x^2 + 7x + 10

Notice how the numerators and denominators have several things in common? That means when you cross-multiply, many of the terms will cancel out.

After cross-multiplying, simplifying, and canceling out terms, you'll get....

4x^2 + 14x = 0

2x(2x + 7) = 0

x = 0, -7/2

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Thu May 24, 2012 9:14 pm
Followed by:1 members

by pitta.deepak » Tue Jul 30, 2013 1:23 am
Step 1: 3/(x+3) + 4/(x+4) = 2/(x+2) + 5/(x+5)

Step 2: 3/(x+3) - 2/(x+2) = 5/(x+5)- 4/(x+4)

Step 3: x/(x+3)(x+2) = x/(x+5)(x+4)

Step 4: (x+3)(x+2) = (x+5)(x+4)

Step 5: Simplify to get x= -7/2

Step 2 is crucial to solve it faster.
Top
Post new topic Post Reply
• Page 1 of 1