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

It is currently 20 Jan 2019, 14:05

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

What is the remainder obtained when 63^25 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 63^25 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 05:32
2
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (01:02) correct 38% (00:44) wrong based on 92 sessions

HideShow timer Statistics

What is the remainder obtained when \(63^{25}\) is divided by 16?

A. -1
B. 0
C. 5
D. 10
E. 15
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 223
Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

Show Tags

New post 29 Oct 2018, 06:22
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15
Intern
Intern
User avatar
B
Joined: 13 Mar 2018
Posts: 24
GPA: 3.12
WE: Project Management (Other)
Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

Show Tags

New post 07 Nov 2018, 09:34
1
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 223
Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

Show Tags

New post 07 Nov 2018, 18:38
AnupamKT wrote:
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.

https://gmatclub.com/forum/all-about-ne ... 91928.html
Manager
Manager
User avatar
G
Joined: 03 Mar 2017
Posts: 211
Reviews Badge CAT Tests
What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

Show Tags

New post 07 Nov 2018, 19:06
AnupamKT wrote:
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.


63^25 can be written as ((64-1)^25)/16

64 is divisible by 16. what is left is -1^25 which turns out to be -1.

Always make numerator in such a manner that it gets divided by denominator.

But remainder can never by negative hence -1+16 (denominator here) gives 15.

Therefore E.
_________________

--------------------------------------------------------------------------------------------------------------------------
All the Gods, All the Heavens, and All the Hells lie within you.

Director
Director
User avatar
P
Joined: 18 Jul 2018
Posts: 575
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

Show Tags

New post 07 Nov 2018, 19:20
AnupamKT wrote:
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.


Remainder is ALWAYS positive. If you ever get a negative remainder. Just add the divisor to the negative remainder.

Ex: What's the remainder when 31 is divided by 16.

32 is completely divisible by 16. Hence for 31 we get a negative remainder of -1. Adding the divisor, we get -1+16 = 15.

Hope it's clear

Posted from my mobile device
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

Intern
Intern
avatar
B
Joined: 02 Sep 2016
Posts: 9
Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

Show Tags

New post 07 Nov 2018, 19:59
Unit place cyclicity of 3 -> 3,9,7,1
and Unit place cyclicity of 7 -> 7,9,3,1.

Now,
(63)^25 / 16 = (3 * 3 * 7)^25 /16
=> (3 * 3 * 7)/16 => 63/16
=> remainder as 15.
GMAT Club Bot
Re: What is the remainder obtained when 63^25 is divided by 16? &nbs [#permalink] 07 Nov 2018, 19:59
Display posts from previous: Sort by

What is the remainder obtained when 63^25 is divided by 16?

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


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®.