NEW HERE? LEARN MORE
closeclose
Last visit was: 03 May 2024, 03:02 It is currently 03 May 2024, 03:02
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 m, [m] is defined to be the remainder when 7m

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93024
Own Kudos [?]: 620887 [5]
Given Kudos: 81741
Send PM
CAT Tests Forum Quiz Mode
For a positive integer m, [m] is defined to be the remainder when 7m [#permalink] New post   22 May 2023, 07:30
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

60% (02:00) correct 40% (02:41) wrong based on 65 sessions
Hide Show timer Statistics
For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
ShowHide Answer
Official Answer
A
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3110
Own Kudos [?]: 4211 [0]
Given Kudos: 1851
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: For a positive integer m, [m] is defined to be the remainder when 7m [#permalink] New post   22 May 2023, 13:54
Bunuel wrote:
For a positive integer m, |m| is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


I. [3n + 1]

Remainder(\(\frac{7(3n + 1) }{ 3}\))

Remainder(\(\frac{7(3n) + (7) }{ 3}\))

Remainder = 1

II. [3n]

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder = 1

III. [3n] + 2

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder = 2

Hence, Only I (Option A)
User avatar
B
pragyanbhuyan999
Intern
Intern
Joined: 27 Jan 2023
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 1
Send PM
For a positive integer m, [m] is defined to be the remainder when 7m [#permalink] New post   19 Jun 2023, 07:30
It should be n instead of m in the first line

Posted from my mobile device
User avatar
G
sanchitb23
Manager
Manager
Joined: 08 Nov 2022
Posts: 77
Own Kudos [?]: 34 [0]
Given Kudos: 56
Send PM
Reviews Badge
Re: For a positive integer m, [m] is defined to be the remainder when 7m [#permalink] New post   20 Jun 2023, 13:31
gmatophobia wrote:
Bunuel wrote:
For a positive integer m, |m| is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


I. [3n + 1]

Remainder(\(\frac{7(3n + 1) }{ 3}\))

Remainder(\(\frac{7(3n) + (7) }{ 3}\))

Remainder = 1

II. [3n]

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder = 1

III. [3n] + 2

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder = 2

Hence, Only I (Option A)


What is the difference between your solution of Case 1 and 2? Both Reminders are 1, Kindly elaborate the explanation

Bunuel , Please provide the Official Explanation of this Question
User avatar
B
ayushiii02
Intern
Intern
Joined: 14 Jan 2023
Posts: 6
Own Kudos [?]: 0 [0]
Given Kudos: 5
Send PM
Re: For a positive integer m, [m] is defined to be the remainder when 7m [#permalink] New post   20 Jun 2023, 13:55
I think case 2 should have zero as the remainder, hence only option A.

Posted from my mobile device
User avatar
B
imorenor
Intern
Intern
Joined: 15 Oct 2022
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 14
Send PM
Re: For a positive integer m, [m] is defined to be the remainder when 7m [#permalink] New post   24 Jun 2023, 21:34
gmatophobia wrote:
Bunuel wrote:
For a positive integer m, |m| is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n + 1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


I. [3n + 1]

Remainder(\(\frac{7(3n + 1) }{ 3}\))

Remainder(\(\frac{7(3n) + (7) }{ 3}\))

Remainder = 1

II. [3n]

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder(\(\frac{7(3n) }{ 3}\))

Remainder = 1

III. [3n] + 2

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder(\(\frac{7(3n+2) }{ 3}\))

Remainder = 2

Hence, Only I (Option A)



Shouldn't it be the remainder of II equal to 0?? thanks!
GMAT Club Bot
gmatclubot
Re: For a positive integer m, [m] is defined to be the remainder when 7m [#permalink]
24 Jun 2023, 21:34
Moderators:
Bunuel
Math Expert
93024 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