Last visit was: 19 Jul 2024, 22:43 It is currently 19 Jul 2024, 22:43
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
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642404 [4]
Given Kudos: 86332
Send PM
Senior Manager
Senior Manager
Joined: 05 Aug 2019
Posts: 317
Own Kudos [?]: 286 [3]
Given Kudos: 130
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Send PM
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3128
Own Kudos [?]: 2814 [1]
Given Kudos: 1511
Location: India
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3401
Own Kudos [?]: 1859 [2]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Send PM
Re: If f(x)/f(x1) = (x2)/(x+1), for all x 0 and f(6) = 81, what is the [#permalink]
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.
McCombs School Moderator
Joined: 26 May 2019
Posts: 325
Own Kudos [?]: 356 [1]
Given Kudos: 151
Location: India
GMAT 1: 690 Q50 V33
Send PM
Re: If f(x)/f(x1) = (x2)/(x+1), for all x 0 and f(6) = 81, what is the [#permalink]
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
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22679 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If f(x)/f(x1) = (x2)/(x+1), for all x 0 and f(6) = 81, what is the [#permalink]
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
Non-Human User
Joined: 09 Sep 2013
Posts: 34037
Own Kudos [?]: 853 [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]
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
Re: If f(x)/f(x1) = (x2)/(x+1), for all x 0 and f(6) = 81, what is the [#permalink]
Moderator:
Math Expert
94421 posts