BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

For a positive integer m, [m] is defined to be the remainder

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Sun Jul 08, 2018 11:49 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[GMAT math practice question]

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 & II only
D.I & III only
E. I, II, &III
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Tue Jul 10, 2018 11:27 am
1 = [3n + 1] means remainder when
$$7\ \left[3n\ +\ 1\right]\ =\ \frac{21\ +\ 7}{3},\ we\ get$$
remainder as 1 , hence [3n + 1 ] = 1

2 = [3n] means remainder when 7 [3n]
= 21n is divided by 3, we get remainder as 0, hence [3n] = 0

3] = [3n] + 2 means remainder when
$$7\ \left[3n\right]+2\ =\ \frac{21n\ +\ 2}{3},\ we\ get\ remainder\ $$
as 2 hence, [3n] + 2
so the expression in 1 yields a value of 1
Therefore, Answer is option A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Moderator
Posts: 2544
Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Jul 10, 2018 6:25 pm
I. [3n+1] means remainder when 7(3n+1) = 21n+7 is divided by 3, we get remainder as 1. Hence [3n+1] = 1.

II. [3n] means remainder when 7(3n) = 21n is divided by 3, we get remainder as 0. Hence [3n] = 2.

III. [3n]+2 means remainder when 7(3n)+2 = 21n + 2 is divided by 3, we get remainder as 2. Hence [3n]+2 = 2.

Hence, only I gives remainder as 1. The correct answer is A.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Tue Jul 10, 2018 11:55 pm
=>

Statement I
7(3n+1) = 21n + 7 = 3(7n+2) + 1
Thus, [3n+1] = 1

Statement II
7(3n) = 21n = 3*7n + 0
Thus, [3n] = 0

Statement III
Since [3n] = 0, we have [3n] + 2 = 2.

Thus, only [3n+1] equals 1.

Therefore, the answer is A.

Answer: A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:15 pm
Max@Math Revolution wrote:[GMAT math practice question]

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 & II only
D.I & III only
E. I, II, &III
Let's analyze each Roman numeral.

I. [3n+1]

[3n+1] is the remainder when 7(3n + 1) = 21n + 7 is divided by 3. Since 21n is divisible by 3, we see that [3n+1] is equal to the remainder when 7 is divided by 3, which is 1. So I is true.

II. [3n]

[3n] is the remainder when 7(3n) = 21n is divided by 3. Since 21n is divisible by 3, we see that the remainder is 0. So II is not true.

III. [3n] + 2

We saw that in Roman numeral II, [3n] has a remainder 0 when it's divided by 3. So [3n] + 2 has a remainder of 2 when it's divided by 3. III is not true.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1