GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Jan 2019, 17:32

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

What is the remainder obtained when 63^26 is divided by 16?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
User avatar
G
Joined: 13 May 2017
Posts: 101
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22
GPA: 3.14
WE: Account Management (Entertainment and Sports)
CAT Tests
What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 05:10
1
3
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:05) correct 30% (01:23) wrong based on 61 sessions

HideShow timer Statistics

What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7198
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 06:35
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10



Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
avatar
G
Joined: 09 Jun 2014
Posts: 218
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Premium Member Reviews Badge
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 06:42
chetan2u wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10



Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C



Hi Chetan sir,

What's the concept of negative remainder?Why don't we assume remainder as 15

and then (63/16)*(63^25)

Bold leaves a remainder of 15 and then no reminader.

I have a concept gap here.Please help.
Intern
Intern
avatar
B
Joined: 03 Oct 2018
Posts: 4
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 06:59
(63^26) /16=(16*4-1)^26/16=(-1)^26=1

So choice C
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4330
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 07:04
prabsahi wrote:
chetan2u wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10



Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C



Hi Chetan sir,

What's the concept of negative remainder?Why don't we assume remainder as 15

and then (63/16)*(63^25)

Bold leaves a remainder of 15 and then no reminader.

I have a concept gap here.Please help.


Dear prabsahi

\(\frac{63}{16} = 15\)

And, \(\frac{63^{26}}{16} = \frac{63}{16}*\frac{63}{16}*\frac{63}{16}*\frac{63}{16}*\frac{63}{16}*\)..........26 Times...

We know that \(\frac{63}{16} = 15\)

So, \(\frac{63}{16}*\frac{63}{16} = \frac{225}{16}\) = Remainder \(1\)

We may save \(\frac{63}{16}*\frac{63}{16}\) will always yeild 1 as remainder and we have 13 such sets of \(\frac{63}{16}*\frac{63}{16}\), thus, the result will be 1 , Answer must be (C) 1

Hope this helps.
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7198
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 07:19
prabsahi wrote:
chetan2u wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10



Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C



Hi Chetan sir,

What's the concept of negative remainder?Why don't we assume remainder as 15

and then (63/16)*(63^25)

Bold leaves a remainder of 15 and then no reminader.

I have a concept gap here.Please help.



Reason, is that you have to get into big calculations then ... say with -1 as remainder we had ODD power 25 then the remainder would be -1, and remainder cannot be negative hence 16-1=15
We are taking negative remainder in initial calculations just to ease our calculations. Otherwise finally it has to be converted into positive remainder.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 509
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User CAT Tests
What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 07:31
2
We can treat it this way

(64-1)^26

64^26 and some lengthy calculations in the end we have 1^26. everything in between 64^26 and 1^26 will be divisible by 16

Everything in this equation is divisible by 16 except for 1 so the remainder is 1

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 07:51
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10


For the concept behind solving such questions, check:
https://www.veritasprep.com/blog/2011/0 ... ek-in-you/

Also for negative remainders, see:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

BSchool Forum Moderator
User avatar
V
Joined: 28 Mar 2017
Posts: 1219
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 08:44
1
VeritasKarishma wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10


For the concept behind solving such questions, check:
https://www.veritasprep.com/blog/2011/0 ... ek-in-you/

Also for negative remainders, see:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/


Both the links are a gem! I still have them bookmarked: these helped me immensely during my preparation phase!
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!
Preparing for RC my way
RC Summary Activity - New Project to imporve RC Skills
Bloomberg's US Bschool Ranking

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant | 2. e-GMAT's ALL SC Compilation | 3. LSAT RC compilation | 4. Actual LSAT CR collection by Broal | 5. QOTD RC (Carcass) | 6. Challange OG RC | 7. GMAT Prep Challenge RC

Manager
Manager
avatar
G
Joined: 09 Jun 2014
Posts: 218
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Premium Member Reviews Badge
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 09:17
chetan2u wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10



Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C


I am not able to understand another point..

I dont see 16 repeated in the denominator.Its occuring only once.
say.. (63/16)*63^25

so first term can give say -1 as remainder later on its just 63^25 times..
Manager
Manager
avatar
G
Joined: 09 Jun 2014
Posts: 218
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Premium Member Reviews Badge
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 09:19
VeritasKarishma wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10


For the concept behind solving such questions, check:
https://www.veritasprep.com/blog/2011/0 ... ek-in-you/

Also for negative remainders, see:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/



Many many many Thanks :)
Intern
Intern
avatar
B
Joined: 03 Oct 2018
Posts: 4
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 09:20
enochjason wrote:
(63^26) /16=(16*4-1)^26/16=(-1)^26=1

So choice C


Also, another approach:
A mod B ( the remainder of A divided by B)
63^25 mod 16
=(16*3+15)^25 mod 16
=15^25 mod 16
=15^(2*12+1) mod 16
=(225^12) * 15 mod 16
=[(16*14+1)^12] *15 mod 16
=(1^12) *15 mod 16
=1*15 mod 16
=15
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7198
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 09:23
prabsahi wrote:
chetan2u wrote:
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10



Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C


I am not able to understand another point..

I dont see 16 repeated in the denominator.Its occuring only once.
say.. (63/16)*63^25

so first term can give say -1 as remainder later on its just 63^25 times..


You multiply the remainders ...
Say a number is 3*5 so when divided by 3 remainders will become 0*2=0
But if number is 4*5.. remainder will become 1*2=2 check 4*5=20and 20 divided by 3 gives a remainder of 2

So you have to divide each term in numerator by the same denominator ...
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
avatar
G
Joined: 09 Jun 2014
Posts: 218
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Premium Member Reviews Badge
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 09:28
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10[/quote]


Hi....
63 divided by 16 will leave a remainder of -1 as 64 is divisible by 16..
So 63*63*63....26times will leave a remainder of (-1)*(-1)*.....26times = \((-1)^{26}=((-1)^2)^{13}=1^{13}=1\)

C[/quote]

I am not able to understand another point..

I dont see 16 repeated in the denominator.Its occuring only once.
say.. (63/16)*63^25

so first term can give say -1 as remainder later on its just 63^25 times..[/quote]

You multiply the remainders ...
Say a number is 3*5 so when divided by 3 remainders will become 0*2=0
But if number is 4*5.. remainder will become 1*2=2 check 4*5=20and 20 divided by 3 gives a remainder of 2

So you have to divide each term in numerator by the same denominator ...[/quote]



Perfect..This was really very helpful.

Many many many Thanks !!
Intern
Intern
avatar
B
Joined: 20 Sep 2018
Posts: 38
Re: What is the remainder obtained when 63^26 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 16:54
rencsee wrote:
What is the remainder obtained when \(63^{26}\) is divided by 16?

A. -2
B. -1
C. 1
D. 8
E. 10


This can be written as -1^26 because 63 leaves 15 or -1 remainder with 16.

-1^even is 1.

Answer is 1. C.
GMAT Club Bot
Re: What is the remainder obtained when 63^26 is divided by 16? &nbs [#permalink] 29 Oct 2018, 16:54
Display posts from previous: Sort by

What is the remainder obtained when 63^26 is divided by 16?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

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

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

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®.