NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 21:52 It is currently 25 Apr 2024, 21:52
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

If 4^16 + 1 is divisible by positive integer x, then which of the foll

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619055 [18]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   14 Apr 2020, 10:00
18
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

38% (02:01) correct 62% (02:19) wrong based on 119 sessions
Hide Show timer Statistics
If \(4^{16} + 1\) is divisible by positive integer x, then which of the following must also be divisible by x?


A. \(4^{96} + 1\)

B. \(4^{48} + 1\)

C. \(4^{32} + 1\)

D. \(4^{16} - 1\)

E. \(4^8 + 1\)

Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
B
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3964 [3]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   14 Apr 2020, 11:52
2
Kudos
1
Bookmarks
Bunuel wrote:
If \(4^{16} + 1\) is divisible by positive integer x, then which of the following must also be divisible by x?


A. \(4^{96} + 1\)

B. \(4^{48} + 1\)

C. \(4^{32} + 1\)

D. \(4^{16} - 1\)

E. \(4^8 + 1\)

Are You Up For the Challenge: 700 Level Questions


y^3 + 1 = (y+1)(y^2 - y +1)

If (y+1) is divisible by x - >( y^3 + 1) will also be divisible by x

4^{16*3} + 1 = 4^48 + 1 will also be divisible by x

IMO B
User avatar
S
gurmukh
Senior Manager
Senior Manager
Joined: 18 Dec 2017
Posts: 270
Own Kudos [?]: 203 [2]
Given Kudos: 20
Send PM
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   14 Apr 2020, 20:54
1
Kudos
1
Bookmarks
a^3 +b^3 =(a+b)(a^2-ab+b^2)

4^48+1= (4^16)^3 +1^3 = (4^16+1)× some integer

Therefore option B is also divisible by x

Posted from my mobile device
User avatar
P
Kritisood
Director
Director
Joined: 21 Feb 2017
Posts: 521
Own Kudos [?]: 1039 [1]
Given Kudos: 1091
Location: India
GMAT 1: 700 Q47 V39
Send PM
Reviews Badge
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   14 Apr 2020, 23:14
If one doesnt remember the formula for a^3+b^3 is there another approach?
User avatar
S
gurmukh
Senior Manager
Senior Manager
Joined: 18 Dec 2017
Posts: 270
Own Kudos [?]: 203 [0]
Given Kudos: 20
Send PM
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   15 Apr 2020, 00:11
Kritisood wrote:
If one doesnt remember the formula for a^3+b^3 is there another approach?

The point is not to know remember the formula because that anyway you can multiply and get the answer. The point is whether you can view the sum from that angle or not. If you remember the value of (a^3+b^3) then that helps you to develop the approach to solve the sum.

Posted from my mobile device
User avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1720
Own Kudos [?]: 1344 [0]
Given Kudos: 607
Location: United States
Send PM
If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   Updated on: 04 Jun 2020, 07:32
Bunuel wrote:
If \(4^{16} + 1\) is divisible by positive integer x, then which of the following must also be divisible by x?

A. \(4^{96} + 1\)
B. \(4^{48} + 1\)
C. \(4^{32} + 1\)
D. \(4^{16} - 1\)
E. \(4^8 + 1\)


(4^(16))^3+(1)^3=(a+b)(a^2+b^2-ab)
(4^(16)+1)((4^(16))^2+1-4^(16))
a+b is div by x

ans (B)

Originally posted by exc4libur on 03 Jun 2020, 09:33.
Last edited by exc4libur on 04 Jun 2020, 07:32, edited 1 time in total.
User avatar
S
gurmukh
Senior Manager
Senior Manager
Joined: 18 Dec 2017
Posts: 270
Own Kudos [?]: 203 [1]
Given Kudos: 20
Send PM
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   03 Jun 2020, 09:56
1
Kudos
exc4libur wrote:
Bunuel wrote:
If \(4^{16} + 1\) is divisible by positive integer x, then which of the following must also be divisible by x?

A. \(4^{96} + 1\)
B. \(4^{48} + 1\)
C. \(4^{32} + 1\)
D. \(4^{16} - 1\)
E. \(4^8 + 1\)


\((4^{16} + 1)/x=(2^{32}+1)/x=p*x\)

\(4^{16} - 1=2^{32}-1=2^{32}-1^2=(2^{32}-1)(2^{32}+1)\)

\((2^{32}-1)(2^{32}+1)/x=p*x*(2^{32}-1)\)

Isn't (D) also correct?

Check your calculation, there is mistake in it..

Posted from my mobile device
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32681
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink] New post   29 Sep 2023, 00:26
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
gmatclubot
Re: If 4^16 + 1 is divisible by positive integer x, then which of the foll [#permalink]
29 Sep 2023, 00:26
Moderators:
Bunuel
Math Expert
92915 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