Last visit was: 12 Dec 2024, 06:43 It is currently 12 Dec 2024, 06:43
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 12 Dec 2024
Posts: 97,845
Own Kudos:
685,276
 [9]
Given Kudos: 88,255
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,845
Kudos: 685,276
 [9]
1
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
User avatar
manpreetsingh86
Joined: 13 Jun 2013
Last visit: 19 Dec 2022
Posts: 222
Own Kudos:
1,100
 [3]
Given Kudos: 14
Posts: 222
Kudos: 1,100
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
pairakesh10
Joined: 10 Jul 2014
Last visit: 28 Feb 2018
Posts: 37
Own Kudos:
61
 [1]
Given Kudos: 35
Concentration: Technology, Strategy
Posts: 37
Kudos: 61
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Ashishmathew01081987
Joined: 20 Jan 2013
Last visit: 07 Jun 2020
Posts: 95
Own Kudos:
287
 [2]
Given Kudos: 71
Status:I am not a product of my circumstances. I am a product of my decisions
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE:Operations (Energy)
Posts: 95
Kudos: 287
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Tough and Tricky questions: Algebra.



If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.


\(f(x) = ax^4 - 4x^2 + ax - 3\)

\(f(b) = ab^4 - 4b^2 + ab - 3\)

\(f(-b) = a(-b)^4 - 4(-b)^2 + a(-b) - 3\)
\(f(-b) = ab^4 - 4b^2 - ab - 3\)

\(f(b) - f(-b) = [ab^4 - 4b^2 + ab - 3] - [ab^4 - 4b^2 - ab - 3]\)
\(f(b) - f(-b) = ab^4 - 4b^2 + ab- 3 - ab^4 + 4b^2+ ab + 3\)
\(f(b) - f(-b) = ab + ab\)
\(f(b) - f(-b) = 2ab\)

Answer is B

avatar
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,551
Own Kudos:
7,513
 [1]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,551
Kudos: 7,513
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\(f(x) = ax^4 – 4x^2 + ax – 3\)

For all even powers, sign would remain the same. For all odd powers, sign would change

\(f(b) - f(-b) = ab^4 - 4b^2 + ab - 3 - (ab^4 - 4b^2 - ab - 3) = 2ab\)

Answer = B
avatar
gmatmo
Joined: 02 Dec 2017
Last visit: 17 May 2019
Posts: 13
Own Kudos:
Given Kudos: 45
Posts: 13
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I do not understand why does a(-b)^4 become ab^4 ??
it has to be -ab^4, doesn't it ?
avatar
AWaheedi
Joined: 30 Jan 2018
Last visit: 24 Jun 2018
Posts: 1
Own Kudos:
2
 [1]
Posts: 1
Kudos: 2
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Substitue the b with any negative number and make that number to the power of 4 and solve for it. You will get a positive figure, as any number to the power of even number will result a positive figure


Sent from my iPhone using GMAT Club Forum
User avatar
mrdlee23
Joined: 29 Jan 2017
Last visit: 02 Dec 2018
Posts: 31
Own Kudos:
Given Kudos: 13
Posts: 31
Kudos: 37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If you look at just -3 then

-3 - (-3) = 0

C, D, and E are out

From there, you can solve until you realize it does not = 0



Bunuel

Tough and Tricky questions: Algebra.



If \(f(x) = ax^4 – 4x^2 + ax – 3\), then \(f(b) – f(-b)\) will equal:


A. 0

B. \(2ab\)

C. \(2ab^4 – 8b^2 – 6\)

D. \(-2ab^4 + 8b^2 + 6\)

E. \(2ab^4 – 8b^2 + 2ab – 6\)


Kudos for a correct solution.
User avatar
niks18
User avatar
Retired Moderator
Joined: 25 Feb 2013
Last visit: 30 Jun 2021
Posts: 887
Own Kudos:
Given Kudos: 54
Location: India
GPA: 3.82
Products:
Posts: 887
Kudos: 1,619
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatmo
I do not understand why does a(-b)^4 become ab^4 ??
it has to be -ab^4, doesn't it ?

hi gmatmo

\((-b)^4=-b*-b*-b*-b\).

In your opinion what should be the result of this multiplication?
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 09 Dec 2024
Posts: 2,044
Own Kudos:
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,044
Kudos: 2,297
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given that \(f(x) = ax^4 – 4x^2 + ax – 3\) and we need to find the value of f(b) – f(–b)

To find f(b) we need to compare what is inside the bracket in f(b) and f(x)

=> We need to substitute x with b in \(f(x) = ax^4 – 4x^2 + ax – 3\) to get the value of f(b)
=> \(f(b) = ab^4 – 4b^2 + a*b – 3\) = \(ab^4 – 4b^2 + ab – 3\)

Similarly, \(f(-b) = a(-b)^4 – 4(-b)^2 + a*(-b) – 3\) = \(ab^4 – 4b^2 - ab – 3\)
=> f(b) - f(-b) = \(ab^4 – 4b^2 + ab – 3\) - (\(ab^4 – 4b^2 - ab – 3\))
= \(ab^4 - ab^4 – 4b^2 + 4b^2 + ab + ab – 3 + 3\) = 2ab

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

Moderator:
Math Expert
97842 posts