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 →

Number Properties w/ Remainders

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Sat Aug 15, 2009 5:10 pm
Thanked: 1 times
by aznmexicana » Tue Jul 20, 2010 10:25 pm
What is the remainder when the positive integer x is divided by 6?

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
2) When x is divided by 12 the remainder is 3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Tue Jul 20, 2010 8:11 am
Thanked: 1 times

by sindhu b » Tue Jul 20, 2010 11:17 pm
IMO D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Tue Jul 20, 2010 11:41 pm
aznmexicana wrote:What is the remainder when the positive integer x is divided by 6?

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
2) When x is divided by 12 the remainder is 3
Like many DS questions, you can solve either by applying concepts or picking numbers. The question is straightforward, so let's dive into the statements.

1) Two key pieces of information.

When x is divided by 2 the remainder is 1 - therefore, x must be odd.
when x is divided by 3, the remainder is 0 - therefore, x must be a multiple of 3.

So, x is an odd multiple of 3: 3, 9, 15, 21, ...

Every one of these numbers gives a remainder of 3 when you divide by 6. Same answer every time, therefore sufficient.

2) Easiest just to pick numbers: 3, 15, 27, 39, ...

Again, we see that all possible values give a remainder of 3 when you divide by 6. Same answer every time, therefore sufficient.

Each statement is sufficient alone: choose (D).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 86
Joined: Mon Sep 13, 2010 2:36 pmFollowed by: 2 members
Thanked: 29 times
GMAT Score:710

by thebigkats » Thu Dec 02, 2010 3:52 pm
agreed. It was pretty straightforward.
1. when X is divided by 3, remainder = 0 means that when you divide it by 6, remainder is either 0 or 3. However given that dividing by 2 gives 1, it must be 3
2. second choice is straightforward. anything that is divided by 12 with remainder of X will have remainder of X or (X-6 if X >=6) when divided by 6. So dividing by 6 will also give us 3

Either one works
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Mon Dec 27, 2010 9:38 am
Thanked: 1 times

by bvosalik » Sat Jan 29, 2011 3:27 am
aznmexicana wrote:What is the remainder when the positive integer x is divided by 6?

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
2) When x is divided by 12 the remainder is 3
Can you please post also the options A-D? thank you :-)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Fri Jan 28, 2011 12:36 am
Thanked: 1 times

by diehard_gmat » Sat Jan 29, 2011 3:46 am
bvosalik wrote:Can you please post also the options A-D? thank you :-)
For GMAT Data Sufficiency Quant problems, there are five answer choices, not four. And the answer choices are always same. The answer choices are,
  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
    (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
    (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    (D) EACH statement ALONE is sufficient.
    (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 131
Joined: Fri Jun 18, 2010 10:19 am
Location: New York, NY
Thanked: 10 times

by aleph777 » Mon Jan 31, 2011 2:09 pm
I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Jan 31, 2011 2:14 pm
aleph777 wrote:I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
Looking at the list of values that satisfy statement 1: 3, 9, 15, 21...

When 3 is divided by 6, the result is 0 R3.
When 9 is divided by 6, the result is 1 R3.
When 15 is divided by 6, the result is 2 R3.

Since R=3 in every case -- including when x=3 -- sufficient.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 86
Joined: Mon Sep 13, 2010 2:36 pmFollowed by: 2 members
Thanked: 29 times
GMAT Score:710

by thebigkats » Mon Jan 31, 2011 2:16 pm
aleph777 wrote:I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
Hi:
When x=3, the remainder upon dividing by 6 = 3. So it is known. Note that the Q says that no is divisible by 3 but not by 2. So it is 3, 9, 15 ... etc. (difference of 6 in consecutive entries). So the remainder when divided by 6 would always be same

So it is D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 131
Joined: Fri Jun 18, 2010 10:19 am
Location: New York, NY
Thanked: 10 times

by aleph777 » Mon Jan 31, 2011 2:16 pm
Wow... I don't know what I was just thinking. Thanks, Mitch.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Mon Dec 27, 2010 9:38 am
Thanked: 1 times

by bvosalik » Wed Feb 02, 2011 2:04 am
diehard_gmat wrote:
bvosalik wrote:Can you please post also the options A-D? thank you :-)
For GMAT Data Sufficiency Quant problems, there are five answer choices, not four. And the answer choices are always same. The answer choices are,
  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
    (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
    (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    (D) EACH statement ALONE is sufficient.
    (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
thank you very much
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members
Thanked: 173 times
GMAT Score:710

by gmatmachoman » Fri Feb 04, 2011 2:24 am
aleph777 wrote:I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
My guess is u would have thought :


1) When x is divided by 2 the remainder is 0, and when x is divided by 3, the remainder is 1

instead of :

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Mon Jan 17, 2011 3:13 pm

by sallywoo » Fri Feb 11, 2011 10:44 am
makes sense! thanks guys!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Sun Feb 27, 2011 1:51 am

by cuty » Sat Mar 26, 2011 10:32 pm
IMO D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 72
Joined: Wed Oct 27, 2010 2:06 amFollowed by: 1 member
Thanked: 2 times

by saurabh2525_gupta » Sat Aug 06, 2011 12:18 am
The answer is D.

We can take values and check with them.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply