NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 09:37 It is currently 25 Apr 2024, 09:37
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618962 [4]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the [#permalink] New post   26 May 2020, 02:42
4
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

78% (02:30) correct 22% (02:19) wrong based on 132 sessions
Hide Show timer Statistics
If \(\frac{f(x)}{f(x−1)} = \frac{(x−2)}{(x+1)}\), for all \(x ≥ 0\) and \(f(6) = 81\), what is the value of \(f(4)\)?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
G
sambitspm
Senior Manager
Senior Manager
Joined: 05 Aug 2019
Posts: 317
Own Kudos [?]: 279 [3]
Given Kudos: 130
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Send PM
Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the [#permalink] New post   26 May 2020, 03:03
1
Kudos
2
Bookmarks
See the attachment -> D
Attachments

1.PNG
1.PNG [ 25.49 KiB | Viewed 3533 times ]

User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [1]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the [#permalink] New post   26 May 2020, 03:32
1
Kudos
F{x}/F{x-1} = (X-2)/(X+1) -----(1)
PUT F(X) = F(6) = 81
F(6)/F(5)= 4/7
F(5) = 81*7/4
F(5) = 567/4 -----(2)

PUT F(5) VALUE IN THE EQUATION (1)
F(5)/F(4) = 3/6
(567/4)/F(4) = 1/2
F(4) = 567*2/4
F(4) = 567/2 => 283.5

ANSWER IS D

Posted from my mobile device
User avatar
L
GMATWhizTeam
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3409
Own Kudos [?]: 1800 [2]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Send PM
Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the [#permalink] New post   26 May 2020, 04:09
2
Kudos
Expert Reply
Bunuel wrote:
If \(\frac{f(x)}{f(x−1)} = \frac{(x−2)}{(x+1)}\), for all \(x ≥ 0\) and \(f(6) = 81\), what is the value of \(f(4)\)?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284



Solution


    • We have \(\frac{f(x)}{f(x-1)} = \frac{(x – 2)}{(x+1)}\)
Substituting x = 6 in the above equation, we get,
    • \(\frac{f(6)}{f(5)} =\frac{4}{7} …………..Eq.(i)\)
Substituting x = 5 in the the given expression, we get,
    • \(\frac{f(5)}{f(4)} =\frac{3}{6} …………..Eq.(ii)\)
Now, from Eq.(i) and Eq.(ii), we can write,
    • \(\frac{f(6)}{f(5)}* \frac{f(5)}{f(4)} =\frac{4}{7}*\frac{3}{6}\)
      \(⟹\frac{f(6)}{f(4)} = \frac{2}{7}\)
      \(⟹f(4) = f(6)* \frac{7}{2} = 81*\frac{7}{2} =283.5\)
Thus, the correct answer is Option D.
User avatar
P
NiftyNiffler
McCombs School Moderator
Joined: 26 May 2019
Posts: 325
Own Kudos [?]: 354 [1]
Given Kudos: 151
Location: India
Schools: INSEAD Jan '20 LSE MFin "21 McCombs '23 Tepper '23
GMAT 1: 690 Q50 V33
Send PM
Reviews Badge
Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the [#permalink] New post   26 May 2020, 09:07
1
Kudos
If f(x)/f(x−1)=(x−2)/(x+1), for all x≥0x≥0 and f(6)=81, what is the value of f(4)?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284

f(6)/f(5) = 4/7

similarly, f(5)/f(4) = 3/6 = 1/2


Multiplying both, f(6)/f(4) = 2/7 => f(4) = 7 * 81/2 = 283.5

So D
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22052 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the [#permalink] New post   30 May 2020, 14:33
Expert Reply
Bunuel wrote:
If \(\frac{f(x)}{f(x−1)} = \frac{(x−2)}{(x+1)}\), for all \(x ≥ 0\) and \(f(6) = 81\), what is the value of \(f(4)\)?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284



First, letting x = 6, we have:

f(6)/f(5) = 4/7

81/f(5) = 4/7

4 * f(5) = 567

f(5) = 567/4

Now, letting x = 5, we have:

f(5)/f(4) = 3/6

(567/4)/f(4) = 1/2

f(4) = 2 * 567/4

f(4) = 567/2 = 283.5

Answer: D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32674
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If f(x)/f(x1) = (x2)/(x+1), for all x 0 and f(6) = 81, what is the [#permalink] New post   07 Oct 2022, 11:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If f(x)/f(x1) = (x2)/(x+1), for all x 0 and f(6) = 81, what is the [#permalink]
07 Oct 2022, 11:36
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions