NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 13:03 It is currently 27 Apr 2024, 13:03
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

(4^8 - 3^8)/(4^4 + 3^4)=

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92954
Own Kudos [?]: 619469 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
(4^8 - 3^8)/(4^4 + 3^4)= [#permalink] New post   14 Feb 2022, 09:15
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (01:10) correct 18% (02:13) wrong based on 55 sessions
Hide Show timer Statistics
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216
ShowHide Answer
Official Answer
D
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29958 [1]
Given Kudos: 799
Location: Canada
Send PM
(4^8 - 3^8)/(4^4 + 3^4)= [#permalink] New post   Updated on: 14 Feb 2022, 10:54
1
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216


Key property (difference of squares): \(x^2 - y^2 = (x+y)(x-y)\)

We can quickly answer the question if we first recognize that \(4^8 - 3^8\) is a difference of squares that can be factored to get:

\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\frac{{(4^4 + 3^4)(4^4 - 3^4)}}{{4^4 + 3^4}}\)

\(=4^4 - 3^4\)

Note: At this point, we can either evaluate \(4^4 - 3^4\) by calculating the individual values of \(4^4\) and \(3^4\), or we can apply one more factorization.
I'm going to apply one more factorization
\(4^4 - 3^4 = (4^2 + 3^2)(4^2 - 3^2)\)
\( = (16 + 9)(16 - 9)\)
\( = (25)(7)\)
\( = 175\)

Answer: D

Originally posted by BrentGMATPrepNow on 14 Feb 2022, 10:37.
Last edited by BrentGMATPrepNow on 14 Feb 2022, 10:54, edited 1 time in total.
User avatar
G
Regor60
Senior Manager
Senior Manager
Joined: 21 Nov 2021
Posts: 437
Own Kudos [?]: 212 [1]
Given Kudos: 345
Send PM
Re: (4^8 - 3^8)/(4^4 + 3^4)= [#permalink] New post   14 Feb 2022, 10:45
1
Kudos
BrentGMATPrepNow wrote:
Bunuel wrote:
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216


Key property (difference of squares): \(x^2 - y^2 = (x+y)(x-y)\)

We can quickly answer the question if we first recognize that \(4^8 - 3^8\) is a difference of squares that can be factored to get:

\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\frac{{(4^4 + 3^4)(4^4 - 3^4)}}{{4^4 + 3^4}}\)

\(=4^4 - 3^4\)

Note: At this point, we can either evaluate \(4^4 - 3^4\) by calculating the individual values of \(4^4\) and \(3^4\), or we can apply one more factorization.
I'm going to apply one more factorization
\(4^4 - 3^4 = (4^2 + 3^2)(4^2 - 3^2)\)
\( = (16 + 9)(16 - 9)\)
\( = (25)(7)\)
\( = 225\)


175, but agree up until then

Posted from my mobile device
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29958 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: (4^8 - 3^8)/(4^4 + 3^4)= [#permalink] New post   14 Feb 2022, 10:56
Expert Reply
Top Contributor
Regor60 wrote:

175, but agree up until then



Thanks for the heads up.
Turns out that multiplying 25 by 7 is the trickiest part of the question!
I've edited my response.

Kudos for you!
User avatar
P
kungfury42
Director
Director
Joined: 07 Jan 2022
Posts: 608
Own Kudos [?]: 446 [0]
Given Kudos: 725
Schools: NUS '25 (A)
GMAT 1: 740 Q51 V38
GPA: 4
Send PM
Reviews Badge
(4^8 - 3^8)/(4^4 + 3^4)= [#permalink] New post   14 Feb 2022, 14:07
Bunuel wrote:
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216


\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}\) = \(\frac{{(4^4 + 3^4)}*{(4^4 - 3^4)}}{{4^4 + 3^4}}\)

= \(4^4 - 3^4\)
= \(256 - 81\)
= \(175\)

Hence, our answer is option D, 175.
GMAT Club Bot
gmatclubot
(4^8 - 3^8)/(4^4 + 3^4)= [#permalink]
14 Feb 2022, 14:07
Moderators:
Bunuel
Math Expert
92955 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