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

 It is currently 15 Oct 2019, 01:56 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  What is the remainder when the positive integer x is divided

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 03 Oct 2008
Posts: 59
What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

9 00:00

Difficulty:   85% (hard)

Question Stats: 53% (02:16) correct 47% (02:10) wrong based on 244 sessions

HideShow timer Statistics

What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

Originally posted by albany09 on 07 Oct 2008, 06:25.
Last edited by Bunuel on 07 Oct 2014, 07:18, edited 1 time in total.
Edited the question and added the OA.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

5
4
albany09 wrote:
What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

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.

There is a very clean approach to solve such questions within a minute and without writing down anything. But for that you need to understand 'Divisibility' well. If you are willing to do that, read these 4 posts first:
http://www.veritasprep.com/blog/2011/04 ... unraveled/
http://www.veritasprep.com/blog/2011/04 ... y-applied/
http://www.veritasprep.com/blog/2011/05 ... emainders/
http://www.veritasprep.com/blog/2011/05 ... s-part-ii/

Now let's look at the question:

What is the remainder when the positive integer x is divided by 8?
This means: What is leftover when you make groups of 8?

Statement 1: When x is divided by 12, the remainder is 5.

When you make groups of 12, 5 balls are leftover. When you make groups of 8 instead, each of the groups of 12 balls leaves 4 balls. If no. of groups of 12 is even, you can combine 2 groups of 4 balls each to make more groups of 8. In that case, 5 balls will be still leftover. So a remainder of 5 is possible.

If no. of groups of 12 is odd, 4 balls will be leftover from one group of 12 and 5 balls will be still leftover. So a total of 9 balls will be leftover. We can make another group of 8 out of these 9 balls and 1 ball will be leftover. So a remainder of 1 is also possible.

Since remainder can be 5 or 1, this statement alone is not sufficient.

Statement 2: When x is divided by 18, the remainder is 11.

When you make groups of 18, 11 balls are leftover. When you make groups of 8 instead, each of the groups of 18 balls makes 2 groups of 8 balls each and leaves 2 balls.
Now there are 4 possibilities:
1. We are left with 2 balls + the original 11 remaining balls = 13 balls
When you make another group of 8 from 13, remainder will be 5
2. We are left with 2+2 balls + the original 11 remaining balls = 15 balls
When you make another group of 8 from 15, remainder will be 7
3. We are left with 2+2+2 balls + the original 11 remaining balls = 17 balls
When you make 2 groups of 8 from 17, remainder will be 1
4. We are left with no groups of 2 balls since they all make a complete group of 8. Only the original 11 balls are remaining. When you make a group of 8 from 11, remainder will be 3.

Since remainder can be 5, 7, 1 or 3, this statement alone is not sufficient.

Using both statements, remainder can be either 5 or 1 so they both together are not sufficient.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
General Discussion
SVP  Joined: 29 Aug 2007
Posts: 1981
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

albany09 wrote:
What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

1: x = 12k + 5
2: x = 18j + 11

1&2: 12k + 5 = 18j + 11
12k - 18j = 6

some integers (such as 29, 65, 101 or so on) fit to the above eq.

29 divided by 8 has 5 as reminder.
65 divided by 5 has 1 as reminder.

so E.
_________________
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT
Intern  Joined: 01 Mar 2006
Posts: 21
Schools: columbia, chicago, Insead, wharton
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

I chose E as well. But, i dont have an approach to solve these kind of problems. Can anyone help ?
Manager  S
Joined: 22 Jan 2014
Posts: 170
WE: Project Management (Computer Hardware)
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

albany09 wrote:
What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

E.

1) x = (12k+5) ; where k is a non-negative integer
(12k+5) mod 8 = (4k+5) mod 8
when k is even, remainder with 8 will be 5
when k is odd, remainder with 8 will be 1
so, insufficient.

2) x = (18p+5) ; where p is a non-negative integer
(18p+5) mod 8 = (2p+5) mod 8
p=0; remainder = 5
p=1; remainder = 7
p=2; remainder = 1
p=3; remainder = 3
p=4; remainder = 5
and then the cycle repeats.
so, insufficient.

(1)+(2) --> 1 & 5 is common in both lists so insufficient again.
_________________
Illegitimi non carborundum.
Senior Manager  B
Joined: 23 Sep 2015
Posts: 371
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38 WE: Real Estate (Mutual Funds and Brokerage)
What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

1
Is my way of doing this correct?:

(1) $$12q + 5 = x$$ insuf

(2) $$18b + 11 = x$$ insuf

Together:
$$12q + 5 = 18b +11$$

$$12q - 18b = 6$$

$$6(2q - 3b) = 6$$

This leads us to $$2q - 3b = 1$$

I replace q by b in equation 1:

$$12(\frac{1 + 3b}{2}) +5 = x$$

$$18b + 11 = x$$

Statement 1 becomes equal to statement 2 : Hence insufficient.
_________________
Intern  Joined: 22 May 2016
Posts: 3
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

x = 8K + r;
1) x = 12P + 5 -> 2 equation, 3 unknown = Can't be solved; insufficient.
2) x = 18Q + 11 -> 2 equation, 3 unknown = Can't be solved; insufficient.

Combine -> 3 equation, 4 unknown = Can't be solved; insufficient.

Option E.

Note: If there can be a way to reduce variable eg. one var is factor of other var, we could have found a solution.
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3583
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

Option 1 : Possible Numbers could be 5,17,29,41,53,65,...

when divided by 8, they will give remainders are 5,1,5,1,...

Hence, not sufficient.

Option 2 : Possible Numbers could be 11,29,47,65,...

when divided by 8, they will give remainders are 3,5,7,5,...

Hence, not sufficient.

Combining both the statements, Possible no. could be 29 and 65.

When divided by 8,They will give remainders as 5,1.

Hence, after combining also, it is insufficient. Correct Answer : E.
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Intern  S
Joined: 10 Jun 2016
Posts: 45
Schools: IIM-A"19
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

My way of doing

x = 8k + r, r = ?

S-1) x = 12k + 5, Possible values x = 5, 17,29. Not sufficient
S-2) x = 18k + 11, x = 11,29. Not sufficient
S-T) Using above 2 statements and LCM of 12 & 18 we get 36 and first common term for the two statements is 29,
x = 36k+29, x = 29, 65. So remainders are 5 or 1. NS.
_________________
Thank You Very Much,
CoolKl
Success is the Journey from Knowing to Doing

A Kudo is a gesture, to express the effort helped. Thanks for your Kudos.
Senior Manager  P
Joined: 29 Jun 2017
Posts: 424
GPA: 4
WE: Engineering (Transportation)
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

x/8 => remainder =?
1) x/12 => R=5
x= 5,17,29,41,53,65,77,89,101...
R= 5,1 ( A,D eliminated)

2) x/18=> R=11
x= 11,47,65,_,_,101,....
R= 3,7 ( B eliminated)

Combine

x= 65,101,...
R= 1,5 ( C eliminated)

E is the Answer
_________________
Give Kudos for correct answer and/or if you like the solution.
Non-Human User Joined: 09 Sep 2013
Posts: 13147
Re: What is the remainder when the positive integer x is divided  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the remainder when the positive integer x is divided   [#permalink] 12 Apr 2019, 16:22
Display posts from previous: Sort by

What is the remainder when the positive integer x is divided

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  