NEW HERE? LEARN MORE
closeclose
Last visit was: 10 May 2024, 07:43 It is currently 10 May 2024, 07:43
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

For a positive integer n, which of the following remainders cannot be

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93152
Own Kudos [?]: 622622 [2]
Given Kudos: 81828
Send PM
CAT Tests Forum Quiz Mode
For a positive integer n, which of the following remainders cannot be [#permalink] New post   02 Feb 2024, 02:30
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

80% (01:41) correct 20% (01:45) wrong based on 105 sessions
Hide Show timer Statistics
For a positive integer n, which of the following remainders cannot be obtained when dividing 12n by 15?

A. 0
B. 3
C. 5
D. 6
E. 9




Show Spoiler
For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?
ShowHide Answer
Official Answer
C
User avatar
G
sood1596
Manager
Manager
Joined: 15 Apr 2020
Posts: 212
Own Kudos [?]: 162 [1]
Given Kudos: 97
Location: United Arab Emirates
Concentration: General Management, Strategy
WE:Analyst (Consulting)
Send PM
Reviews Badge
Re: For a positive integer n, which of the following remainders cannot be [#permalink] New post   02 Feb 2024, 03:57
1
Kudos
IMO answer is C

because we get remainders as 0,3,6,9 in multiples of 2,3,4 and 5
User avatar
G
Shubhradeep
Manager
Manager
Joined: 11 Jan 2024
Posts: 121
Own Kudos [?]: 158 [4]
Given Kudos: 90
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.14
Send PM
Re: For a positive integer n, which of the following remainders cannot be [#permalink] New post   02 Feb 2024, 12:03
3
Kudos
1
Bookmarks
Correct option should be C

We can try out values to rule out 5 as a remainder but there is a beautiful way to find out that 5 cannot be the remainder when 12n is divided by 15.

We can reduce \(\frac{12n}{15}\) to \(\frac{4n}{5}\) by dividing both numerator and denominator by 3. Now you divide any number by 5, you get 5 remainders which are 0,1,2,3,4.
But Note that these are not the remainders when 12n is divided by 15. We should not forget to multiply these numbers (i.e, 0,1,2,3,4) by 3 because we divided numerator and denominator both by 3. C'mon man you take something in maths you should give something back!! :lol:

So, the possible remainders are -> 0,3,6,9,12 (You can check it out with values I won't put my effort to spoil your effort)
Hence, 5 is not a possible remainder.

Hence, correct option should be C
User avatar
S
PranavVyas
Manager
Manager
Joined: 13 Aug 2020
Posts: 75
Own Kudos [?]: 66 [0]
Given Kudos: 86
Concentration: Marketing, Operations
Schools: IIM-A '24 IIMB '25
GMAT 1: 540 Q15 V29
WE:Operations (Manufacturing)
Send PM
Forum Quiz Mode
For a positive integer n, which of the following remainders cannot be [#permalink] New post   Updated on: 04 Feb 2024, 18:54
Number 15 divisible by 5 , others not have such possible remainder.

IMO-C "5"

Originally posted by PranavVyas on 02 Feb 2024, 19:03.
Last edited by PranavVyas on 04 Feb 2024, 18:54, edited 1 time in total.
User avatar
P
VivekPrateek
Senior Manager
Senior Manager
Joined: 01 May 2022
Posts: 435
Own Kudos [?]: 402 [1]
Given Kudos: 100
Location: India
WE:Engineering (Computer Software)
Send PM
Re: For a positive integer n, which of the following remainders cannot be [#permalink] New post   02 Feb 2024, 21:49
1
Kudos
Bunuel wrote:
For a positive integer n, which of the following remainders cannot be obtained when dividing 12n by 15?

A. 0
B. 3
C. 5
D. 6
E. 9


This is a PS Butler Question



Show Spoiler
For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?

Attachments

Screenshot_20240203_101839_Samsung Notes.jpg
Screenshot_20240203_101839_Samsung Notes.jpg [ 263.16 KiB | Viewed 1016 times ]

GMAT Club Bot
gmatclubot
Re: For a positive integer n, which of the following remainders cannot be [#permalink]
02 Feb 2024, 21:49
Moderators:
Bunuel
Math Expert
93150 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