Last visit was: 02 Jan 2026, 13:51 It is currently 02 Jan 2026, 13:51
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

(3^2+1)(81^2+1)(9^2+1)(3^2−1)=

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 34323
Own Kudos [?]: 40694 [1]
Given Kudos: 26657
Send PM
(3^2+1)(81^2+1)(9^2+1)(3^2−1)= [#permalink] New post   18 Feb 2021, 04:25
1
Expert Reply
00:00

Question Stats:

74% (01:41) correct 25% (02:03) wrong based on 59 sessions

Hide Show timer Statistics

\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)

A. \(81^4+1\)

B. \(9^9−1\)

C. \(3^{16}−1\)

D. \(3^{32}−1\)

E. \(3^{96}+1\)


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
ShowHide Answer
Official Answer
C
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12581 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: (3^2+1)(81^2+1)(9^2+1)(3^2−1)= [#permalink] New post   18 Feb 2021, 06:05
1
1
Bookmarks
Carcass wrote:
\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)

A. \(81^4+1\)

B. \(9^9−1\)

C. \(3^{16}−1\)

D. \(3^{32}−1\)

E. \(3^{96}+1\)


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


This question tests our ability to recognize a potential difference of squares.
That is: (a + b)(a - b) = a² - b²

(3² + 1)(81² + 1)(9² + 1)(3² − 1) = (3² + 1)(3² − 1)(9² + 1)(81² + 1)
= (9 + 1)(9 − 1)(9² + 1)(81² + 1)
= (9² − 1)(9² + 1)(81² + 1)
= (81 - 1)(81 + 1)(81² + 1)
= (81² - 1)(81² + 1)
= 81⁴ - 1
Check the answer choices......81⁴ - 1 is not among the answer choices. We'll have to REWRITE our answer...
81⁴ - 1 = (3⁴)⁴ - 1
= 3¹⁶ - 1

Answer: C
User avatar
D
KarunMendiratta
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3668 [1]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
(3^2+1)(81^2+1)(9^2+1)(3^2−1)= [#permalink] New post   18 Feb 2021, 06:15
1
Carcass wrote:
\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)

A. \(81^4+1\)

B. \(9^9−1\)

C. \(3^{16}−1\)

D. \(3^{32}−1\)

E. \(3^{96}+1\)



\((9 + 1) (9^4 + 1) (9^2 + 1) (9 - 1)\)

\((9^2 - 1) (9^2 + 1) (9^4 + 1)\)

\((9^4 - 1) (9^4 + 1)\)

\((9^8 - 1\)

\((3^2)^8 - 1\)

\(3^{16} - 1\)

Hence, option C
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5702
Own Kudos [?]: 82 [0]
Given Kudos: 0
Send PM
Re: (3^2+1)(81^2+1)(9^2+1)(3^21)= [#permalink] New post   02 Oct 2022, 01:33
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
gmatclubot
Re: (3^2+1)(81^2+1)(9^2+1)(3^21)= [#permalink]
02 Oct 2022, 01:33
Moderators:
adewale223
GRE Instructor
137 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1141 posts
VibhuAnurag
GRE Instructor
234 posts
Nsp10
Moderator
40 posts
tyrant100
GRE Forum Moderator
126 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact