Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 20:23

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is an integer and n^4 is divisible by 32, which of the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
User avatar
Joined: 18 Feb 2010
Posts: 174
Schools: ISB
Followers: 4

Kudos [?]: 105 [1] , given: 0

GMAT Tests User
If n is an integer and n^4 is divisible by 32, which of the [#permalink] New post 03 Mar 2010, 00:35
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (02:28) correct 30% (01:11) wrong based on 115 sessions
If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10
[Reveal] Spoiler: OA

_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!


Last edited by Bunuel on 23 Oct 2013, 23:44, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Director
Director
avatar
Joined: 20 Sep 2006
Posts: 658
Followers: 2

Kudos [?]: 60 [0], given: 7

GMAT Tests User
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Mar 2010, 06:39
Given:
n^4/32 = int
n^4/2^5 = int
1/2(n/2)^4 = int

try n= int = 2,4,6,8... becuase n/2 must be an integer

n=2 wont work because 1/2(n/2)^4 needs to be an integer.
n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)
n=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the remainder of n/32 = remainder of 16x8/32 = 4 (option B)

Once you understand that the question is asking 1/2(n/2)^4 must be an integer then you can quickly run the numbers and figure out the remainder of n/32.
Manager
Manager
avatar
Joined: 10 Aug 2009
Posts: 123
Followers: 3

Kudos [?]: 12 [0], given: 13

Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Mar 2010, 07:10
rao_1857 wrote:
Given:
n^4/32 = int
n^4/2^5 = int
1/2(n/2)^4 = int

try n= int = 2,4,6,8... becuase n/2 must be an integer

n=2 wont work because 1/2(n/2)^4 needs to be an integer.
n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)
n=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the remainder of n/32 = remainder of 16x8/32 = 4 (option B)

Once you understand that the question is asking 1/2(n/2)^4 must be an integer then you can quickly run the numbers and figure out the remainder of n/32.


Maybe I'm missing something but why are you calculating the result, and then getting the remainder of the result divided by 32? Shouldn't you be getting the remainder of n divided by 32?
For example, using your statement above:
n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)
Result is indeed 8, but you need to divide 4 by 32 (0 remainder 4), not 8 by 32

If its done the way I described above, the answer could be A, D or E
Manager
Manager
avatar
Joined: 29 Dec 2009
Posts: 122
Location: india
Followers: 1

Kudos [?]: 13 [0], given: 10

GMAT Tests User
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Mar 2010, 07:33
2^4=16 so not possible
and 2^5 = 32

so v need (2^2)^2

4 satisfies this condition
Manager
Manager
avatar
Joined: 26 May 2005
Posts: 210
Followers: 2

Kudos [?]: 63 [0], given: 1

GMAT Tests User
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Mar 2010, 08:32
mustdoit wrote:
If n is an integer and n4 is divisible by 32, which of the following could be the remainder when n is divided by 32?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10


Solving this would clarify lots of concepts !!! Solution coming....

32 = 2^5
n^4/32 is an integer

n^4 is even and at the minimum (n^4 and n) should be a multiple of 4.

so the min value of n is 4 and remainder is 4

B
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18856
Followers: 3275

Kudos [?]: 22916 [7] , given: 2651

Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Mar 2010, 12:51
7
This post received
KUDOS
Expert's post
mustdoit wrote:
If n is an integer and n4 is divisible by 32, which of the following could be the remainder when n is divided by 32?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10


Solving this would clarify lots of concepts !!! Solution coming....


Given: n^4=32k=2^5k --> n=2\sqrt[4]{2k} --> as n is an integer, the least value of n is obtained when k=8 --> n_{min}=2\sqrt[4]{2*8}=4 --> \frac{n_{min}}{32}=\frac{4}{32} gives remainder of 4.

Answer: B.

To elaborate more: as n is an integer and n=2\sqrt[4]{2k}, then \sqrt[4]{2k} must be an integer. So n can take the following values: 4 for k=8, 8 for k=2^3*2^4, 12 for k=2^3*3^4... Basically n will be multiple of 4. So \frac{n}{32} can give us the reminder of 4, 8, 12, 16, 20, 24, 28, 0 - all multiples of 4. Only multiple of 4 in answer choices is 4.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 30 Jun 2004
Posts: 178
Location: Singapore
Followers: 1

Kudos [?]: 10 [0], given: 5

GMAT ToolKit User GMAT Tests User
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Mar 2010, 23:15
Bunuel!! Thanks for the explanation.
1 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [1] , given: 235

GMAT Tests User Reviews Badge
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 04 Mar 2010, 06:03
1
This post received
KUDOS
IMO B

Take n^4 = 2^5 * K where K can be of form K = 2^{4m-5}

=> n = 2^m

now m can be any integer greater than 1
( m cannot be 1 as K is an integer thus, 4m-5 > 0 )

now m=2,3,4....so on gives n =4, 8 , 16........36, 40... so on

now 4 can be the remainder when n=36.

Since we are dividing by 32, remainder must be multiple of 4 as n is multiple of 4.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

1 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [1] , given: 235

GMAT Tests User Reviews Badge
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 27 Aug 2010, 09:50
1
This post received
KUDOS
I have made typo mistakes and that makes it bad solution. I dont rem where I was dreaming that day.
Since n^4 is divisible by 32 =>

n^4 = 32*A but for n to be an integer 32*A should be reduced to an integer when we take 4th root on both sides
thus 32*A must be of the form 2^{4z}
=> A = 2^{4z-5}
=> n is of the form 2^z

forz =1 , 4z-5 <0 thus not possible.
for z = 2 , n = 4

when 4 is divided by 32 the remainder is 4.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Director
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 693
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 14

Kudos [?]: 69 [0], given: 15

GMAT Tests User
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Sep 2010, 20:48
Gurpreet,
Can you please explain why does 32A be of the form 2^(4z)? Thanks
_________________

Consider kudos, they are good for health

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 901 [0], given: 235

GMAT Tests User Reviews Badge
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 03 Sep 2010, 21:58
mainhoon wrote:
Gurpreet,
Can you please explain why does 32A be of the form 2^(4z)? Thanks


32*A = n^4 and n is integer. take 4th root on both the sides.

Both LHS and RHS should have integral values. This is only possible when 32A = 2^{4z}
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Manager
avatar
Joined: 16 Mar 2010
Posts: 191
Followers: 2

Kudos [?]: 37 [0], given: 9

GMAT Tests User
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 04 Sep 2010, 23:00
Always use method explained by bunuel above in this type of the problems
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1835
Followers: 167

Kudos [?]: 33 [0], given: 0

Premium Member
Re: n^4 is divisible by 32. Find remainder for n/32 [#permalink] New post 23 Oct 2013, 21:12
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 886
Concentration: General Management, General Management
Schools: IIM A '15
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
Followers: 12

Kudos [?]: 166 [0], given: 300

Premium Member CAT Tests
Re: If n is an integer and n^4 is divisible by 32, which of the [#permalink] New post 19 Apr 2014, 21:18
Concept Tested :

Remainders

background:

a*b*c/d then

if Rem(a/d) =x, Rem(b/d)=y, Rem(c/d)=z then

x*y*z/d

Sol:

Try numbers using options.

(1). 2

means 32+2 =34

REM(34*34*34*34/32) must be 0

REM(2*2*2*2/32) is 16

(2). 4

means 32+4=36

REM(36*36*36*36/32) must be 0

REM(4*4*4*4/32) is 0

Hence the answer
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Re: If n is an integer and n^4 is divisible by 32, which of the   [#permalink] 19 Apr 2014, 21:18
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If n is an integer, is n + 4 a prime number? metallicafan 6 18 Nov 2011, 09:15
12 Experts publish their posts in the topic If n is an integer and n^4 is divisible by 32, which of the mustdoit 13 03 Mar 2010, 00:35
When n^4 is divided by 32 the remainder is 0. If n is mbaorbust08 5 19 Nov 2007, 15:39
if k and n are integers, is n divisible by 7? 1. n-3=2k 2. bmwhype2 4 03 May 2007, 22:35
If n is an integer and n^4 is divisible by 32, which of the FN 5 12 Sep 2005, 12:18
Display posts from previous: Sort by

If n is an integer and n^4 is divisible by 32, which of the

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.