When the positive integer x is divided by 11, the quotient : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 07:20

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# When the positive integer x is divided by 11, the quotient

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

### Hide Tags

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1310
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 79

Kudos [?]: 1003 [1] , given: 157

When the positive integer x is divided by 11, the quotient [#permalink]

### Show Tags

13 Apr 2010, 04:49
1
This post received
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:43) correct 31% (02:00) wrong based on 487 sessions

### HideShow timer Statistics

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A. 4
B. 3
C. 2
D. 1
E. 0
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93247 [6] , given: 10555

Re: Remainder Problem [#permalink]

### Show Tags

13 Apr 2010, 05:07
6
This post received
KUDOS
Expert's post
12
This post was
BOOKMARKED
Hussain15 wrote:
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A.4
B.3
C.2
D.1
E.0

(1) When the positive integer x is divided by 11, the quotient is y and the remainder 3 --> $$x=11y+3$$;
(2) When x is divided by 19, the remainder is also 3 --> $$x=19q+3$$.

Subtract (2) from (1) --> $$19q=11y$$ --> $$y=\frac{19q}{11}$$. Now as $$y$$ and $$q$$ are integers and 19 is prime $$\frac{q}{11}$$ must be an integer --> $$y=19*integer$$ --> $$y$$ is a multiple of 19, hence when divide by 19 remainder is 0.

Answer: E.
_________________
Senior Manager
Joined: 24 Jul 2009
Posts: 297
Followers: 3

Kudos [?]: 130 [2] , given: 0

Re: Remainder Problem [#permalink]

### Show Tags

13 Apr 2010, 05:40
2
This post received
KUDOS
1
This post was
BOOKMARKED
Hussain15 wrote:
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A.4
B.3
C.2
D.1
E.0

IMHO E

We have two cases.. x = 11*y + 3
and x = 19*m + 3... where just like y..its an integer..

equating both the equations..
11*y + 3 = 19*m + 3
y = 19*m / 11. now both 11 and 19 are prime...so m has to be a multiple of 11.. Only then we can get y as integer.. so let say m= 11*p, where p is a positive integer..

so y = (19 * 11 * p)/11 and when y is divide by 19..we get remainder as zero.

OA plz..
Manager
Joined: 29 Oct 2009
Posts: 201
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Followers: 2

Kudos [?]: 92 [0], given: 12

Re: Remainder Problem [#permalink]

### Show Tags

13 Apr 2010, 06:03
x=11*k + 3, where 11*k = y
x=19*m + 3

=> 11*k +3 = 19*m+3
=> y+3 = 19*m + 3
=> y = 19*m
So y is divisible by 19 with 0 remainder.

Answer is E.
_________________

+1Kudos, if this helps

Manager
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 70
WE 1: 6 years - Consulting
Followers: 3

Kudos [?]: 46 [5] , given: 27

Re: Remainder Problem [#permalink]

### Show Tags

10 Sep 2010, 02:07
5
This post received
KUDOS
Any Number which when divided by divisor d1,d2, etc. leaving same remainder "r" takes the form of "K+r"
where k = LCM (d1,d2)

In this case the divisors are 11 & 19 and remainder is 3.
so LCM (11,19) = 209
So N= 209+3 = 212
Also X=d1q+3 ; which means d1q=209 & d1=11 therefore q=19

And ( y divided by 19)19/19 leaves remainder 0.

Answer is E

This approach took me less than 50 secs. hope it helps.
_________________

Consider giving Kudos if my post helps in some way

Veritas Prep GMAT Instructor
Joined: 26 Jul 2010
Posts: 240
Followers: 215

Kudos [?]: 487 [0], given: 29

Re: Remainder Problem [#permalink]

### Show Tags

10 Sep 2010, 13:39
Hey guys,

Looks like this question is under control - I liked seeing that subject line since I just threw up a blog post specifically on remainders today. If you're interested, you can see it at: http://blog.veritasprep.com/2010/09/gmat-tip-of-week-remainder.html
_________________

Brian

Save \$100 on live Veritas Prep GMAT Courses and Admissions Consulting

Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Joined: 15 Apr 2010
Posts: 195
Followers: 2

Kudos [?]: 17 [0], given: 29

Re: Remainder Problem [#permalink]

### Show Tags

10 Sep 2010, 14:28
great explanation Bunuel... thanks!
Intern
Joined: 07 Jul 2010
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Help w/ Remainder Question (MGMAT Online Question Bank) [#permalink]

### Show Tags

29 Nov 2010, 21:15
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A) 0
B) 1
C) 2
D) 3
E) 4

So I got this far:

If x divided by 11 has a quotient of y and a remainder of 3, x can be expressed as x = 11y + 3, where y is an integer (by definition, a quotient is an integer). If x divided by 19 also has a remainder of 3, we can also express x as x = 19z + 3, where z is an integer.

We can set the two equations equal to each other:
11y + 3 = 19z + 3
11y = 19z

This is where I get lost

How does 11y = 19z help me determine what the remainder is when y is divided by 19???? Is there another step somewhere?

Here's the rest of the explanation:

The question asks us what the remainder is when y is divided by 19. From the equation we see that 11y is a multiple of 19 because z is an integer. y itself must be a multiple of 19 since 11, the coefficient of y, is not a multiple of 19.

Answer is A) 0

Please tell me there's an easier way to do this then to "assume" y is a multiple of 19 so then there's no remainder. Thoughts??

Thanks in advance!
Manager
Joined: 13 Jul 2010
Posts: 169
Followers: 1

Kudos [?]: 73 [0], given: 7

Re: Help w/ Remainder Question (MGMAT Online Question Bank) [#permalink]

### Show Tags

29 Nov 2010, 21:34
both 11 and 19 are prime numbers therefore z and y have to be multiples of these prime numbers in order for 11y=19Z to be true. Since there prime there is no other way possible. And if y is a multiple of Y, then Y/19 will result in a 0 remainder.
Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 772 [0], given: 33

Re: Help w/ Remainder Question (MGMAT Online Question Bank) [#permalink]

### Show Tags

29 Nov 2010, 22:17
From given conditions:

11y + 3 = 19q +3

11y = 19q

This implies y = q

y = q = 0 is the only possibility.

Therefore when Y = 0 is divided by 19, the remainder is 0
Manager
Status: I rest, I rust.
Joined: 04 Oct 2010
Posts: 122
Schools: ISB - Co 2013
WE 1: IT Professional since 2006
Followers: 17

Kudos [?]: 119 [1] , given: 9

Re: Help w/ Remainder Question (MGMAT Online Question Bank) [#permalink]

### Show Tags

29 Nov 2010, 22:37
1
This post received
KUDOS
continued from 11y=19z

z = 11y/19

we know that z is a quotient and hence a whole number

For z to be a whole number 11y has to be divisible by 19. now since 11 is not divisible by 19, Y has to be..

PS: If you like my post click on +1Kudos
_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

Intern
Joined: 05 Oct 2010
Posts: 13
Followers: 0

Kudos [?]: 0 [0], given: 19

Dividing By 11 and 19 [#permalink]

### Show Tags

27 Dec 2010, 15:42
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A) 0
B) 1
C) 2
D) 3
E) 4

Could you please explain the answer??
I am confused by the following explanation:

If x divided by 11 has a quotient of y and a remainder of 3, x can be expressed as x = 11y + 3, where y is an integer (by definition, a quotient is an integer). If x divided by 19 also has a remainder of 3, we can also express x as x = 19z + 3, where z is an integer.

We can set the two equations equal to each other:
11y + 3 = 19z + 3
11y = 19z

The question asks us what the remainder is when y is divided by 19. From the equation we see that 11y is a multiple of 19 because z is an integer. y itself must be a multiple of 19 since 11, the coefficient of y, is not a multiple of 19.

If y is a multiple of 19, the remainder must be zero.

The correct answer is A.
Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93247 [0], given: 10555

Re: Dividing By 11 and 19 [#permalink]

### Show Tags

27 Dec 2010, 15:47
Merging similar topics. Please ask if anything remains unclear.
_________________
Intern
Joined: 12 Dec 2010
Posts: 14
Schools: Wharton, Columbia, Booth, NYU
Followers: 0

Kudos [?]: 24 [1] , given: 0

Re: Remainder Problem [#permalink]

### Show Tags

27 Dec 2010, 18:42
1
This post received
KUDOS
We know by now..
11y + 3 = 19z + 3
=> 11y = 19z

11 and 19 are prime numbers, so to hold the above equation correct, y has to be multiple of 19 and z has to be multiple of 11

11 * 19 = 19 * 11
11 * 38 = 19 * 22
11 * 57 = 19 * 33
and so on..

Basically, y can be 19, 38, 57... which is divisible by 19.
_________________

Practice, More Practice, Still More Practice... THE only way to succeed!!!
+1Kudos, if this helps with your preparation. Good luck!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13461
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: When the positive integer x is divided by 11, the quotient [#permalink]

### Show Tags

16 Oct 2013, 13:23
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.
_________________
Manager
Joined: 28 Apr 2013
Posts: 159
Location: India
GPA: 4
WE: Medicine and Health (Health Care)
Followers: 1

Kudos [?]: 68 [0], given: 84

Re: Remainder Problem [#permalink]

### Show Tags

16 Dec 2013, 22:50
Bunuel wrote:
Hussain15 wrote:
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A.4
B.3
C.2
D.1
E.0

(1) When the positive integer x is divided by 11, the quotient is y and the remainder 3 --> $$x=11y+3$$;
(2) When x is divided by 19, the remainder is also 3 --> $$x=19q+3$$.

Subtract (2) from (1) --> $$19q=11y$$ --> $$y=\frac{19q}{11}$$. Now as $$y$$ and $$q$$ are integers and 19 is prime $$\frac{q}{11}$$ must be an integer --> $$y=19*integer$$ --> $$y$$ is a multiple of 19, hence when divide by 19 remainder is 0.

Answer: E.

Thanks or the explanation.
Hw you figured out q/11 is an integer. I know that q is an integer and 11 also; but cannot guarantee that q/ 11 - will be an integer. Please clarify.

_________________

Thanks for Posting

LEARN TO ANALYSE

+1 kudos if you like

Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93247 [0], given: 10555

Re: Remainder Problem [#permalink]

### Show Tags

17 Dec 2013, 00:55
rango wrote:
Bunuel wrote:
Hussain15 wrote:
When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?

A.4
B.3
C.2
D.1
E.0

(1) When the positive integer x is divided by 11, the quotient is y and the remainder 3 --> $$x=11y+3$$;
(2) When x is divided by 19, the remainder is also 3 --> $$x=19q+3$$.

Subtract (2) from (1) --> $$19q=11y$$ --> $$y=\frac{19q}{11}$$. Now as $$y$$ and $$q$$ are integers and 19 is prime $$\frac{q}{11}$$ must be an integer --> $$y=19*integer$$ --> $$y$$ is a multiple of 19, hence when divide by 19 remainder is 0.

Answer: E.

Thanks or the explanation.
Hw you figured out q/11 is an integer. I know that q is an integer and 11 also; but cannot guarantee that q/ 11 - will be an integer. Please clarify.

Let me ask you a question: how can y be an integer if $$\frac{q}{11}$$ is not?
_________________
Manager
Joined: 28 Apr 2013
Posts: 159
Location: India
GPA: 4
WE: Medicine and Health (Health Care)
Followers: 1

Kudos [?]: 68 [0], given: 84

Re: Remainder Problem [#permalink]

### Show Tags

17 Dec 2013, 03:18
Let me ask you a question: how can y be an integer if $$\frac{q}{11}$$ is not?[/quote]

Ok BUT Since x= 11(y) + 3 and x= 19 (q) + 3 ; it means that 11 is greater than q. therefor the result q/ 11 will be fraction not an integer.

Let me what you think of
_________________

Thanks for Posting

LEARN TO ANALYSE

+1 kudos if you like

Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93247 [0], given: 10555

Re: Remainder Problem [#permalink]

### Show Tags

17 Dec 2013, 06:13
rango wrote:
Let me ask you a question: how can y be an integer if $$\frac{q}{11}$$ is not?

Ok BUT Since x= 11(y) + 3 and x= 19 (q) + 3 ; it means that 11 is greater than q. therefor the result q/ 11 will be fraction not an integer.

Let me what you think of[/quote]

That's not correct.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13461
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: When the positive integer x is divided by 11, the quotient [#permalink]

### Show Tags

17 Dec 2014, 11:15
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: When the positive integer x is divided by 11, the quotient   [#permalink] 17 Dec 2014, 11:15

Go to page    1   2    Next  [ 24 posts ]

Similar topics Replies Last post
Similar
Topics:
7 When positive integer x is divided by 5, the quotient is q and the rem 5 31 Oct 2016, 06:58
8 When positive integer x is divided by 11, the quotient is y and the re 7 31 Mar 2015, 04:45
8 When positive integer N is divided by positive integer P, the quotient 5 27 Feb 2015, 04:59
32 When the positive integer x is divided by 11, the quotient 16 21 Jan 2012, 00:21
6 When the integer n is divided by 17, the quotient is x and t 10 03 Apr 2011, 04:45
Display posts from previous: Sort by

# When the positive integer x is divided by 11, the quotient

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.