Quadratic Equation - Why is this the answer?

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sat Aug 11, 2012 1:31 am

Quadratic Equation - Why is this the answer?

by Poisson » Sun Jul 10, 2016 5:08 am
Please see the attached picture. I don't understand why crossing the respective numerators and denominators and multiplying the denominators doesn't work for this problem. For example, I know that a/b + c/d = (ad+bc)/bd. I tried using this method but did not get the correct answer. Please help me understand. Thank you!
Attachments
Quadratic Equation - Question for BTG.jpg

Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sat Aug 11, 2012 1:31 am

by Poisson » Sun Jul 10, 2016 5:11 am
Attached is a copy of my work. The answer is B but I got D and E using the shortcut for getting common denominators. Any help would be greatly appreciated.
Attachments
quad work.jpeg

GMAT/MBA Expert

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] » Sun Jul 10, 2016 5:37 am
Hi Poisson,

If you take a good look at the first two 'lines' of your work, you'll see that you just removed the denominators from the calculation (and then you just combined the numerators) - that is NOT mathematically correct. If you want to approach this question algebraically, then that's your choice (although it will be a lot of work!), but you have to combine like terms before you 'cancel out' a fraction. You would likely find it MUCH faster to TEST VALUES (try TESTing A=2 or A=4 and track the results).

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Apr 26, 2014 10:53 am
Thanked: 16 times
Followed by:4 members
GMAT Score:780

by 800_or_bust » Sun Jul 10, 2016 5:49 am
Poisson wrote:Attached is a copy of my work. The answer is B but I got D and E using the shortcut for getting common denominators. Any help would be greatly appreciated.
You were good up to the point where you combined the fraction, but then you cancelled terms that couldn't be cancelled. And where did the 0 come from? That expression does not equal zero. It equals one of the answer choices.
800 or bust!

Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Apr 26, 2014 10:53 am
Thanked: 16 times
Followed by:4 members
GMAT Score:780

by 800_or_bust » Sun Jul 10, 2016 6:03 am
The correct way to approach this algebraically would be to factor out a -1 from the denominator of the second term as follows:

((a^2 + 12) / (a-3)) + (7a / (3-a)) = ((a^2 + 12) / (a-3)) + (7a / ((-1)(a-3))

Now the -1 can be freely moved to the numerator, so it simplifies as follows:

((a^2 + 12) / (a-3)) + (-7a / (a-3))

Now we have a common denominator and are able to add the numerators:

(a^2 - 7a + 12) / (a-3)

Factor the quadratic expression in the numerator:

(a-3)(a-4)/(a-3)

And cancel like terms.

The answer is a-4.
800 or bust!

Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Apr 26, 2014 10:53 am
Thanked: 16 times
Followed by:4 members
GMAT Score:780

by 800_or_bust » Sun Jul 10, 2016 6:09 am
Remember for all a & b, a - b = - (b - a). And (a-b)^2 = (b-a)^2, because squaring always produces a positive result and each of those expressions have the same absolute value.
800 or bust!

User avatar
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 » Sun Jul 10, 2016 9:57 am
If a=0, then (a²+12)/(a-3) + 7a/(3-a) = (0+12)/(0-3) + 0 = -4.
Now plug a=0 into the answer choices to see which yields a result of -4.
Only B works:
a-4 = 0-4 = -4.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3