GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Oct 2019, 20:28

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42
GPA: 3.82
f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 31 Jan 2019, 02:16
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (02:07) correct 45% (02:25) wrong based on 38 sessions

HideShow timer Statistics

[GMAT math practice question]

\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\). What is \(f(x)\)?

\(A. f(x) = \frac{( x + 5 )}{( x – 3 )}\)
\(B. f(x) = \frac{( x - 5 )}{( x + 3 )}\)
\(C. f(x) = \frac{( x + 5 )}{( x + 3 )}\)
\(D. f(x) = \frac{( x – 5 )}{( x – 3 )}\)
\(E. f(x) = \frac{( x + 3 )}{( x – 3 )}\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
NUS School Moderator
avatar
V
Joined: 18 Jul 2018
Posts: 1028
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Reviews Badge
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 31 Jan 2019, 03:04
f(2x-1) = f(x)
Now we have to replace 2x-1 by x, i.e, 2x-1 = x
then x = 1
f(2x-1) = -3

Now put x = 1 in all the options, Only Option A yields -3.

A is the answer.
_________________
Press +1 Kudos If my post helps!
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4976
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 31 Jan 2019, 03:06
1
MathRevolution wrote:
[GMAT math practice question]

\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\). What is \(f(x)\)?

\(A. f(x) = \frac{( x + 5 )}{( x – 3 )}\)
\(B. f(x) = \frac{( x - 5 )}{( x + 3 )}\)
\(C. f(x) = \frac{( x + 5 )}{( x + 3 )}\)
\(D. f(x) = \frac{( x – 5 )}{( x – 3 )}\)
\(E. f(x) = \frac{( x + 3 )}{( x – 3 )}\)


from given answer options
do plugin of f(x) as f(2x-1)
in option A
we get
\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\)

IMO A
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Senior Manager
Senior Manager
avatar
G
Joined: 04 Aug 2010
Posts: 474
Schools: Dartmouth College
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 31 Jan 2019, 04:21
MathRevolution wrote:
[GMAT math practice question]

\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\). What is \(f(x)\)?

\(A. f(x) = \frac{( x + 5 )}{( x – 3 )}\)
\(B. f(x) = \frac{( x - 5 )}{( x + 3 )}\)
\(C. f(x) = \frac{( x + 5 )}{( x + 3 )}\)
\(D. f(x) = \frac{( x – 5 )}{( x – 3 )}\)
\(E. f(x) = \frac{( x + 3 )}{( x – 3 )}\)


Let x=1.
Plugging x=1 into \(f(2x-1) = \frac{x + 2}{x – 2}\), we get:
\(f(2*1-1) = \frac{1 + 2}{1 – 2}\)
\(f(1) = -3\)

When x=1, the question stem becomes:
What is \(f(1)\)?
Since f(1) = -3, the correct answer must yield -3 when x=1.
Only A works:
\(f(1) = \frac{1 + 5}{1-3}\) = -3


_________________
GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 31 Jan 2019, 05:39
MathRevolution wrote:
[GMAT math practice question]

\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\). What is \(f(x)\)?

\(A. f(x) = \frac{( x + 5 )}{( x – 3 )}\)
\(B. f(x) = \frac{( x - 5 )}{( x + 3 )}\)
\(C. f(x) = \frac{( x + 5 )}{( x + 3 )}\)
\(D. f(x) = \frac{( x – 5 )}{( x – 3 )}\)
\(E. f(x) = \frac{( x + 3 )}{( x – 3 )}\)

\(? = f\left( x \right)\)

\(f\left( {2x - 1} \right) = {{x + 2} \over {x - 2}}\,\,\,\,\,\left( * \right)\)


\(2x - 1 = y\,\,\,\,\, \Rightarrow \,\,\,\,x = {{y + 1} \over 2}\)

\(\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,f\left( y \right)\,\, = \,\,{{{{y + 1} \over 2} + 2} \over {{{y + 1} \over 2} - 2}}\,\, = \,\,{{y + 1 + 4} \over {y + 1 - 4}} = {{y + 5} \over {y - 3}}\)


\(?\,\,\,:\,\,\,f\left( y \right) = {{y + 5} \over {y - 3}}\,\,\,\,\,\,\,\left[ {\,f\left( x \right) = {{x + 5} \over {x - 3}}\,\,\,{\rm{if}}\,\,{\rm{you}}\,\,{\rm{prefer}}!\,} \right]\)


The correct answer is therefore (A).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 04 Feb 2019, 05:40
=>

We solve this problem using a change of variable. Let \(t = 2x -1.\)
Then \(2x = t + 1\) or \(x = \frac{( t + 1 )}{2.}\)
\(f(2x-1) = f(t) = ( (t+1)/2 + 2 ) / ( (t+1)/2 – 2 ) = ( t + 1 + 4 ) / ( t + 1 – 4 )\)(after multiplying both top and bottom by 2)
\(= \frac{( t + 5 )}{( t – 3 ).}\)
Making the substitution \(t = x\) gives
\(f(x) = \frac{( x + 5 )}{( x – 3 )}.\)

Therefore, the answer is A.
Answer: A
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

Show Tags

New post 06 Feb 2019, 19:34
MathRevolution wrote:
[GMAT math practice question]

\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\). What is \(f(x)\)?

\(A. f(x) = \frac{( x + 5 )}{( x – 3 )}\)
\(B. f(x) = \frac{( x - 5 )}{( x + 3 )}\)
\(C. f(x) = \frac{( x + 5 )}{( x + 3 )}\)
\(D. f(x) = \frac{( x – 5 )}{( x – 3 )}\)
\(E. f(x) = \frac{( x + 3 )}{( x – 3 )}\)


Let y = 2x - 1, so x = (y + 1)/2. In other words,

f(y) = [(y + 1)/2 + 2] / [(y + 1)/2 - 2]

f(y) = (y + 1 + 4) / (y + 1 - 4)

f(y) = (y + 5) / (y - 3)

Now we can replace y with x and obtain:

f(x) = (x + 5) / (x - 3)

Alternate Solution:

First, let’s take x = -2 in f(2x - 1) = (x + 2) / (x - 2):

f( 2(-2) - 1) = (-2 + 2) / (-2 - 2)

f( -5) = 0

Looking at the answer choices, we observe that only A and C equal zero when x = -5; therefore we eliminate B, D and E.

Next, let’s take x = 3 in f(2x - 1) = (x + 2) / (x - 2):

f( 2(3) - 1) = (3 + 2) / (3 - 2)

f(5) = 5

In answer choice C, when we take x = 5, we obtain f(5) = 10/8, which is not equal to 5. Therefore, we eliminate C as well. The only remaining answer choice is A. Indeed, for the function in A, if we take x = 5, we obtain f(5) = (5 + 5) / (5 - 3) = 10/2 = 5.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?   [#permalink] 06 Feb 2019, 19:34
Display posts from previous: Sort by

f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne