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

 It is currently 22 Jul 2018, 02:03

### 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

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

# What is the remainder when the positive integer n is divided by 6?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47167
What is the remainder when the positive integer n is divided by 6?  [#permalink]

### Show Tags

03 Dec 2017, 01:04
00:00

Difficulty:

25% (medium)

Question Stats:

80% (00:45) correct 20% (01:23) wrong based on 45 sessions

### HideShow timer Statistics

What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1

_________________
Manager
Joined: 24 Nov 2016
Posts: 148
Re: What is the remainder when the positive integer n is divided by 6?  [#permalink]

### Show Tags

03 Dec 2017, 10:07
Bunuel wrote:
What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1

(1) n/12 = 12q + 1/12: so n could be {1,13,25,37...} and the numbers in this set divided by 6 all give a remainder of 1. sufficient.
(2) n/3 = 3q + 1/3: so n could be {1,4,7,10,13...} and the numbers in this set divided by 6 give a remainder of 1 or 4. not suf.
CEO
Joined: 12 Sep 2015
Posts: 2633
Re: What is the remainder when the positive integer n is divided by 6?  [#permalink]

### Show Tags

03 Dec 2017, 10:20
Top Contributor
Bunuel wrote:
What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1

Target question: What is the remainder when the positive integer n is divided by 6?

Statement 1: n when divided by 12 leaves a remainder of 1
USEFUL RULE #1: "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

No onto the question...........
Statement 1 does not tell us the quotient, so let's just say that n divided by 12 equals k with remainder 1
So, we can write: n = 12k + 1, where k is some integer
We can also write 12k a different way: n = (6)(2)(k) + 1
Or n = (6)(2k) + 1
As you can see, (6)(2k) is a multiple of 6, which means (6)(2k) + 1 is ONE MORE than a multiple of 6
So, when (6)(2k) + 1 (aka n) is divided by 6, the remainder must be 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n when divided by 3 leaves a remainder of 1
USEFUL RULE #2: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for statement 2, some possible values of n are: 1, 4, 7, 10, 13, 16, 19, 22, etc.
Let's TEST some values...
Case a: If n = 1, then the remainder is 1, when n is divided by 6
Case b: If n = 4, then the remainder is 4, when n is divided by 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 19 Oct 2013
Posts: 12
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: What is the remainder when the positive integer n is divided by 6?  [#permalink]

### Show Tags

04 Dec 2017, 00:38
From 1) we know $$\frac{n}{12} = x + \frac{1}{12}$$ so adjusting it to become $$n = 12x + 1$$ if we let $$x = 0$$ then$$n = 1$$, plug in in the question stem $$\frac{1}{6}$$ remainder is 1, if we let $$x = 1$$, then $$n = 13$$, plug in $$\frac{13}{6} = 2 \frac{1}{6}$$ another remainder of 1 and so it goes. A is sufficient.

From 2) $$\frac{n}{3} = x + \frac{1}{3}$$ so adjusting it to become $$n = 3x + 1$$ if we let $$x = 0$$ then $$n = 1$$, plug in in the question stem $$\frac{1}{6}$$ remainder is 1, if we let $$x = 1$$, then $$n = 4$$, plug in question stem $$\frac{4}{6}$$ a remainder of 4. Because we get two different answers it is insufficient.

Re: What is the remainder when the positive integer n is divided by 6? &nbs [#permalink] 04 Dec 2017, 00:38
Display posts from previous: Sort by

# Events & Promotions

 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®.