function malfunction

Expert replies

jzw: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Mon Feb 13, 2012 3:02 pmFollowed by: 3 members; Thanked: 2 times

by jzw » Sat Mar 03, 2012 12:03 pm

I don't get what I'm not getting. I do understand the concept of functions, they don't "scare me" per se, but I can't understand why the answer choice is D and not A. Meaning, doesn't 1/1/6 become 6? Because you multiply the numerator and denominator by 6/1 in order to get rid of the 1/ ?

Attachments

Like this post

Source: Beat The GMAT — Problem Solving | Sat Mar 03, 2012 12:03 pm

bajjuri6: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Aug 10, 2011 3:40 pm

by bajjuri6 » Sat Mar 03, 2012 12:27 pm

I think it may be easier if you tear up the problem into smaller bits. For this particular one, you must find g(2) and g(x) first. g(x) is given.

=> 1/g(x) = (x - 1) / (x^2 + 2)

g(2) = ((2^2) + 2)/(2-1) = 6

=> 1/g(2) = 1/6

So, 1/g(2) * 1/g(x) = (1/6) * (x-1)/(x^2 + 2)

So, the 6 must be in the denominator. Hope this helps.

Like this post

jzw: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Mon Feb 13, 2012 3:02 pmFollowed by: 3 members; Thanked: 2 times

by jzw » Sat Mar 03, 2012 12:46 pm

thanks for the response. i realized somewhere between my post and you're response that it was just careless math on my part which contributed to the error. thanks!

Like this post

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

by GMATGuruNY » Sat Mar 03, 2012 12:49 pm

jzw wrote:I don't get what I'm not getting. I do understand the concept of functions, they don't "scare me" per se, but I can't understand why the answer choice is D and not A. Meaning, doesn't 1/1/6 become 6? Because you multiply the numerator and denominator by 6/1 in order to get rid of the 1/ ?

Let x=2.
Then g(x) = g(2) = (2Â² + 2)/(2-1) = 6.
Thus, 1/(g(2)) * 1/(g(x)) = 1/6 * 1/6 = 1/36. This is our target.

Now we plug x=2 into the answers to see which yields our target of 1/36.
Only answer choice D works:
(x-1) / 6(xÂ²+2) = (2-1) / 6(2Â²+2) = 1/36.

The correct answer is D.

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

Like this post

jzw: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Mon Feb 13, 2012 3:02 pmFollowed by: 3 members; Thanked: 2 times

by jzw » Sat Mar 03, 2012 5:01 pm

GMATGuruNY wrote:Thus, 1/(g(2))= 1/6

REALLY happy to do plugging in here instead of solving "normally". But how is 1/(g(2)) = 1/6 ?

I get everything else - just this part is messing me up. I would have thought this becomes 12 (6 x 2). What am I missing? Thanks again, in advance.

Like this post

alexander.vien: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Dec 05, 2012 3:24 pm; Thanked: 3 times

by alexander.vien » Mon Jan 21, 2013 5:34 pm

If you think the answer choice is A, then I think the step that you're missing is on the second function, 1/g(x).

When we plug in (x^2+2)/(x-1) into 1/g(x) it's equivalent to division, so we must flip the expression and multiply it by 1 (also known as taking the reciprocal). Thus, we have (x-1)/(x^2+2).

To get 1/g(2) we must simply plug in 2 into the expression and then put a 1 over the result. So,

(2^2 + 2)/(2-1) = 6

So, g(2) = 6

Putting all this information together, 1/6 * (x-1)/(x^2+2) = (x-1)/6(x^2+2)

Answer choice D

Like this post

buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pmFollowed by: 1 member; Thanked: 13 times; GMAT Score:710

by buzzdeepak » Tue Jan 22, 2013 11:20 am

g(2) = 6 (substituting x = 2 in the given equation)

Therefore, 1/g(2) * 1/g(x) = 1 / 6 * (x-1) / (x^2 + 2) = (x-1) / (6*(x^2 + 2))

Remember that both are reciprocals of the original equation. I think that's the only catch.

(Another method is compute g(2)*g(x) = 6 * given function and take reciprocal.)
Hope this helps...

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review