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

 It is currently 22 Oct 2019, 10:07 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.  When the positive integer x is divided by 11, the quotient is y and th

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

Hide Tags

Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45 GPA: 2.9
WE: Information Technology (Consulting)
When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

3
26 00:00

Difficulty:   45% (medium)

Question Stats: 69% (02:01) correct 31% (02:35) wrong based on 522 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. 0
B. 1
C. 2
D. 3
E. 4

Guys struggling to solve this. But this is the concept I am trying to apply:

We can extrapolate a general statement from this form. When dividing x by y, the quotient is q and the remainder is r:
x/y = q + r/y

From there, we can solve for x:
x = qy + r (thats the general form of x = 3(integer) + 1)
Or the quotient:
q = x-r/y

Or, even, the remainder itself:
r = x - qy

But I am getting stuck in finding y when x is divided by 19. Can someone please help?? I don't have an OA either.

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert V
Joined: 02 Sep 2009
Posts: 58426
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

25
15
enigma123 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) 0
B) 1
C) 2
D) 3
E) 4

If you decide to go with quotient/remainder formula approach, then I'd suggest to express the info in the stem with it. And then look whether we can somehow manipulate with the expressions at hand to answer the question.

(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 --> $$x=19q+3$$.

Easy to spot that $$19q+3=11y+3$$ --> $$19q=11y$$ --> $$y=\frac{19q}{11}$$. Now as $$y$$ and $$q$$ are integers and 19 is prime then $$\frac{q}{11}$$ must be an integer --> $$y=19*integer$$ --> $$y$$ is a multiple of 19, hence when divide by 19 remainder is 0.

Hope its clear.
_________________
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

6
1
enigma123 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. 0
B. 1
C. 2
D. 3
E. 4

Guys struggling to solve this. But this is the concept I am trying to apply:

We can extrapolate a general statement from this form. When dividing x by y, the quotient is q and the remainder is r:
x/y = q + r/y

From there, we can solve for x:
x = qy + r (thats the general form of x = 3(integer) + 1)
Or the quotient:
q = x-r/y

Or, even, the remainder itself:
r = x - qy

But I am getting stuck in finding y when x is divided by 19. Can someone please help?? I don't have an OA either.

Take LCM of 19 & 11 = 209
Adding 3 = 212
Say x = 212

212/11: Quotient = 19 (=y) & remainder = 3

212/19: Quotient = 11 & remainder = 3

19/19: Quotient = 1 & remainder = 0 = Answer = A
_________________
Kindly press "+1 Kudos" to appreciate General Discussion
Current Student Joined: 08 Jan 2009
Posts: 287
GMAT 1: 770 Q50 V46 Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

2
Find some numbers that fit the question.

We are told that x and y both give a remainder of 3 when divided by 19 or 11.

We can easily construct a number that fits this.

x = 19*11 + 3

x / 11 = 19 + 3 / 19

so y = 19

remainder when y / 19 is 0

A
Director  Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

2
enigma123 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. 0
B. 1
C. 2
D. 3
E. 4

Sol: Given x=11y+3 or y= (x-3)/11
Also x=19a+3 Substitute for x in the above equation we get

y= (19a+3-3)/11 or y=19a/11. Note that "a" is an integer and multiple of 11

y/19 =a/11 where a/11 is an integer and hence remainder is 0

Ans is A
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

enigma123 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. 0
B. 1
C. 2
D. 3
E. 4

Guys struggling to solve this. But this is the concept I am trying to apply:

We can extrapolate a general statement from this form. When dividing x by y, the quotient is q and the remainder is r:
x/y = q + r/y

From there, we can solve for x:
x = qy + r (thats the general form of x = 3(integer) + 1)
Or the quotient:
q = x-r/y

Or, even, the remainder itself:
r = x - qy

But I am getting stuck in finding y when x is divided by 19. Can someone please help?? I don't have an OA either.

Please find the solution as attached,
Attachments

File comment: www.GMATinsight.com Sol5.jpg [ 76.73 KiB | Viewed 15809 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

enigma123 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. 0
B. 1
C. 2
D. 3
E. 4

19z + 3 = x = 11y + 3

Or, x = 19*11 + 3 { z = 11 and y = 19 }

or, x = 202

y/19 = Quotient 1 and remainder 0

Hence , answer will be (A) 0

Hope this helps !!

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Senior SC Moderator V
Joined: 14 Nov 2016
Posts: 1348
Location: Malaysia
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

Bunuel wrote:
enigma123 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) 0
B) 1
C) 2
D) 3
E) 4

If you decide to go with quotient/remainder formula approach, then I'd suggest to express the info in the stem with it. And then look whether we can somehow manipulate with the expressions at hand to answer the question.

(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 --> $$x=19q+3$$.

Easy to spot that $$19q+3=11y+3$$ --> $$19q=11y$$ --> $$y=\frac{19q}{11}$$. Now as $$y$$ and $$q$$ are integers and 19 is prime then $$\frac{q}{11}$$ must be an integer --> $$y=19*integer$$ --> $$y$$ is a multiple of 19, hence when divide by 19 remainder is 0.

Hope its clear.

Bunuel, what is the relationship between prime and divider in this case?
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Math Expert V
Joined: 02 Sep 2009
Posts: 58426
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

ziyuenlau wrote:
Bunuel wrote:
enigma123 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) 0
B) 1
C) 2
D) 3
E) 4

If you decide to go with quotient/remainder formula approach, then I'd suggest to express the info in the stem with it. And then look whether we can somehow manipulate with the expressions at hand to answer the question.

(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 --> $$x=19q+3$$.

Easy to spot that $$19q+3=11y+3$$ --> $$19q=11y$$ --> $$y=\frac{19q}{11}$$. Now as $$y$$ and $$q$$ are integers and 19 is prime then $$\frac{q}{11}$$ must be an integer --> $$y=19*integer$$ --> $$y$$ is a multiple of 19, hence when divide by 19 remainder is 0.

Hope its clear.

Bunuel, what is the relationship between prime and divider in this case?

We have $$y=\frac{19q}{11}$$. 19 is not a multiple of 11, thus for 19q/11 to be an integer q must be a multiple of 11.
_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15309
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

1
Hi All,

We're told that...
X/11 = Y remainder 3
X/19 = something remainder 3

With the first piece of information, we know that X is 3 greater than a multiple of 11; with the second piece of information, we know that X is 3 greater than a multiple of 19. To have a remainder of 3 when you divide X by BOTH 11 and 19, X must be a number that is 3 greater than a MULTIPLE of BOTH 11 and 19.

We're asked what the remainder would be when Y is divided by 19. At this point, you might recognize that you could choose Y=19 and solve from there. If you don't recognize why that that relationship exists, then here's a more step-heavy way to get to the correct answer:

X = (11)(19) + 3 = 209 + 3 = 212

212/11 = Y remainder 3
212 = 11Y + 3
209 = 11Y
209/11 = Y
19 = Y

We're ultimately asked what the remainder would be when 19 is divided by 19. The remainder is 0.

GMAT assassins aren't born, they're made,
Rich
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4017
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

1
Top Contributor
enigma123 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. 0
B. 1
C. 2
D. 3
E. 4

A fast approach is to find a value of x that meets the given conditions.

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....
Notice that x = 3 meets the above conditions.
3 divided by 11 = 0 with remainder 3. In this case, y = 0
Likewise, 3 divided by 11 also leaves a remainder of 3

What is the remainder when y is divided by 19?
In the above example, y = 0
So, when we divide 0 by 19, the remainder is 0

RELATED VIDEO FROM OUR COURSE

_________________
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: When the positive integer x is divided by 11, the quotient is y and th  [#permalink]

Show Tags

enigma123 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. 0
B. 1
C. 2
D. 3
E. 4

We can create the following expressions:

x = 11y + 3

and

x = 19Q + 3

Thus:

11y + 3 = 19Q + 3

11y = 19Q

11y/19 = Q

Since Q is an integer and 11 is not divisible by 19, then y must be divisible by 19, and hence the remainder when y is divided by 19 is zero.

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13409
Re: When the positive integer x is divided by 11, the quotient  [#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: When the positive integer x is divided by 11, the quotient   [#permalink] 16 Feb 2019, 02:54
Display posts from previous: Sort by

When the positive integer x is divided by 11, the quotient is y and th

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

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