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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Status: Finally Done. Admitted in Kellogg for 2015 intake

Joined: 25 Jun 2011

Posts: 505

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
[#permalink]

Show Tags

21 Jan 2012, 01:21

3

23

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

73% (01:22) correct 27% (02:05) wrong based on 678 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 (thats 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.

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.

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

Show Tags

10 Mar 2014, 21:54

3

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 (thats 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

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

Show Tags

10 Mar 2014, 23:31

Can we argue that this is a poorly written question? I was always taught that the quotient was the result of division. At first I paused thinking they must mean just the integer, even though I'd never seen that definition used. Then I decided that must be the "trick" of the question, that y is in fact the answer to x/11.

I got

x = 212

y = 19 + 3/11 = 212/11

y/19 = 212/11 * 1/19 = 212/209 = 1 R 3

The trick would be that people would misinterpret the question and mistake y as 19. But if y is x/11, then we will only have the same remainder when x is a multiple of 19 and 11. (Multiple of 19) + 3 yields a remainder of 3 when 19 is the divisor. Basically, the question would be testing only logic and, in theory, you would never have to figure out any values at all.

So I input the answer as 3, which is not the OA.

Afterward, I looked it up and quotient can also refer to just the integer of the result.

My question: Would this ever be a real GMAT question? We are taught (at least in American schools) that quotient is not just integer, but integer and remainder. Thus, the question appears ambiguous to me and probably a large segment of other GMAT takers. Thoughts?

Edit:

Just consulted OG: "For example, when 28 is divided by 8, the quotient is 3 and the remainder is 4 since 28 = (8)(3) + 4" (p. 108). OG for GRE says something similar. I just find it bizarre that at no time in my formal education did anyone give this definition.

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

Show Tags

11 Mar 2014, 05:11

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.”

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

Show Tags

29 Aug 2016, 10:30

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 (thats 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 11053 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

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

Show Tags

Updated on: 26 Jan 2018, 19:11

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

least value of x=3 3/11 gives a quotient of 0 y=0 0/19 leaves a remainder of 0 A

Originally posted by gracie on 29 Aug 2016, 12:14.
Last edited by gracie on 26 Jan 2018, 19:11, edited 1 time in total.

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

Show Tags

16 Oct 2016, 11:44

A is the correct answer. Here's why:

From the prompt we can derive two equations:

x=11y+3 x=19z+3

From this we can set the two equal to each other, leaving us with...

11y=19z --> manipulate further to give... 11 = (19z)/y --> From this we know that z must equal 11 and y must equal 19 in order for the equation to hold. Therefore, since y = 19, dividing by 19 will give a remainder of 0

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

Show Tags

06 Nov 2016, 15:34

Hey Everyone. There are two methods that can be used here as far as i know.

First => x=11y+3 and x=19z+3 for some integer z Hence 11y+3=19z+3 11y=19z => z=11y/19 as z needs to be an integer => y must be a multiple of 19. Hence the remainder that y leaves with 19 must be zero.

Second => You see this is a problem solving question. We will have only one answer. x=19y+3 x=11z+3 hence combing the equations => x= 3+11*19*p for some integer p. smallest possible value of x is 3 for the y is zero. so y=0 is a acceptable value. what is the remainder when 0 is divided by 19 ? Its zero. as every number divides 0. Hence the answer must be zero.

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

Show Tags

07 Nov 2016, 13:53

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

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

Show Tags

19 Jan 2017, 04:22

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.

Answer: A.

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."

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

Show Tags

19 Jan 2017, 05:56

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.

Answer: A.

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.
_________________

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

Show Tags

28 Aug 2017, 00:49

Such questions are disaster as they take a lot of time solving. but here is a shorter way i.e through equations. x/ 11 yields remainder 3 and quotient y. so we can form equation

x= 11y + 3 ........(1)

also we know that when x is divided by 19, remainder is same. let's take "a" as a quotient.

x=19a +3 .........(2) equating 1 and 2 11y+3= 19a+3 11y=19a

since both 19 and 11 are prime numbers, with no number in common, so the only values a and y can get are y=19 and a=11

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.

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

Show Tags

04 Jul 2018, 07:28

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

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

Show Tags

04 Jul 2018, 10:29

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

3+(11*19)=212=x 212/11 gives a quotient of 19=y 19/19 leaves a remainder of 0 A

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

Show Tags

25 Jul 2018, 17:51

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.

Answer: A
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions