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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

When the positive integer x is divided by 11, the quotient [#permalink]
13 Apr 2010, 04:49

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

71% (02:42) correct
29% (02:06) wrong based on 328 sessions

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?

Re: Remainder Problem [#permalink]
13 Apr 2010, 05:07

8

This post received KUDOS

Expert's post

6

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.

Re: Remainder Problem [#permalink]
13 Apr 2010, 05:40

2

This post received KUDOS

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.

Re: Remainder Problem [#permalink]
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

Re: Remainder Problem [#permalink]
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 _________________

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

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

Dividing By 11 and 19 [#permalink]
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.

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

Re: Remainder Problem [#permalink]
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.

Re: Remainder Problem [#permalink]
17 Dec 2013, 00:55

Expert's post

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? _________________

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

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

In out-of-the-way places of the heart, Where your thoughts never think to wander, This beginning has been quietly forming, Waiting until you were ready to emerge. For a long...