Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
02 Oct 2019, 07:51
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (03:28) correct
75%
(01:33)
wrong
based on 8
sessions
History
Date
Time
Result
Not Attempted Yet
A function f(x) is defined as (x + 1) × f(x + 1) + x × f(x) + (x – 1) × f(x – 1) = 0 for x ≥ 2 . If f(1) = 40
and f(6) = 180, find the value of f(14).
(a) –80
(b) –160
(c) –1120
(d) Cannot be determined
and f(6) = 180, find the value of f(14).
(a) –80
(b) –160
(c) –1120
(d) Cannot be determined
05 Oct 2019, 05:13
Kudos
Bookmarks
The question is about finding pattern in the function. I tried with f(6) and I wanted to reduce it to f(1), but i found an interesting pattern in between.
Putting x=5 to get x+1 = 6
6f(6) + 5f(5) + 4f(4) = 0 ... (1)
Now we need to reduce f(5) to smaller f()'s
so, putting x=4 to get x+1=5
5f(5) + 4f(4) + 3f(3) = 0 .... (2)
(1) - (2) we get
6f(6) + 5f(5) + 4f(4) - (5f(5) + 4f(4) + 3f(3)) = 0
6f(6) - 3f(3) = 0 => 6f(6) = 3f(3)
Now this is where I realize that there can be a pattern where each number xf(x) = (x-3)f(x-3), I wan't to conclude this so i will try to get this for one more pattern
putting x=3 to get x+1 =4
4f(4) + 3f(3) + 2f(2) = 0 ...(3)
(2) - (3) we get
5f(5) + 4f(4) + 3f(3) - (4f(4) + 3f(3) + 2f(2)) = 0
5f(5) - 2f(2) = 0 => 5f(5) = 2f(2), so again we have proved that xf(x) = (x-3)f(x-3)
So, we will conclude that it is true for all x >= 4 (As x-3 min can be 1, so x>=4)
Similarly, 14f(14) = 11f(11) = 8f(8) = 5f(5) ...(4)
Now, we need to find 5f(5)
Using (1)
6f(6) + 5f(5) + 4f(4) = 0
I know that 4f(4) = 1f(1) = 40 (given)
f(6) = 180 (given)
and 5f(5) = 14f(14) (from (4) )
=> 6*180 + 14f(14) + 40 = 0
1080 + 14f(14) + 40 = 0
14f(14) = -1120
f(14) = -1120/14 = -80
So, answer will be A
Hope it helps!
To learn more about Functions watch this video
Putting x=5 to get x+1 = 6
6f(6) + 5f(5) + 4f(4) = 0 ... (1)
Now we need to reduce f(5) to smaller f()'s
so, putting x=4 to get x+1=5
5f(5) + 4f(4) + 3f(3) = 0 .... (2)
(1) - (2) we get
6f(6) + 5f(5) + 4f(4) - (5f(5) + 4f(4) + 3f(3)) = 0
6f(6) - 3f(3) = 0 => 6f(6) = 3f(3)
Now this is where I realize that there can be a pattern where each number xf(x) = (x-3)f(x-3), I wan't to conclude this so i will try to get this for one more pattern
putting x=3 to get x+1 =4
4f(4) + 3f(3) + 2f(2) = 0 ...(3)
(2) - (3) we get
5f(5) + 4f(4) + 3f(3) - (4f(4) + 3f(3) + 2f(2)) = 0
5f(5) - 2f(2) = 0 => 5f(5) = 2f(2), so again we have proved that xf(x) = (x-3)f(x-3)
So, we will conclude that it is true for all x >= 4 (As x-3 min can be 1, so x>=4)
Similarly, 14f(14) = 11f(11) = 8f(8) = 5f(5) ...(4)
Now, we need to find 5f(5)
Using (1)
6f(6) + 5f(5) + 4f(4) = 0
I know that 4f(4) = 1f(1) = 40 (given)
f(6) = 180 (given)
and 5f(5) = 14f(14) (from (4) )
=> 6*180 + 14f(14) + 40 = 0
1080 + 14f(14) + 40 = 0
14f(14) = -1120
f(14) = -1120/14 = -80
So, answer will be A
Hope it helps!
To learn more about Functions watch this video
Moderator:
