Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Jul 2015, 03:45

### 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

# Events & Promotions

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

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

Author Message
TAGS:
Director
Joined: 23 May 2008
Posts: 839
Followers: 3

Kudos [?]: 40 [0], given: 0

When the positive integer x is divided by 11, the quotient [#permalink]  28 Aug 2008, 15:51
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?

0
1
2
3
4
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 577 [0], given: 19

Re: mgmat [#permalink]  28 Aug 2008, 18:13
bigtreezl 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?

0
1
2
3
4

A. has to be 0.

since 11 and 19 both are primes and x = 11y+3 = 19k+3, 11y = 19k.

to have 11y = 19k, y must be 19 or its multiple and k has to be 11 and its multiple. for ex:

if y = 19, k = 11
if y = 38, k = 22

and so on. if so, y yeilds 0 reminder when y is divided by 19.
_________________
Current Student
Joined: 11 May 2008
Posts: 560
Followers: 7

Kudos [?]: 59 [0], given: 0

Re: mgmat [#permalink]  28 Aug 2008, 18:24
i think 0.
cos , both 11 and 19 are prime nos..
so the no that when divided by both of them , which leaves a remainder 3 is the LCM of 11 and 19 = 209.
so 209+3 = 211 is the reqd no. x

211/11 = 19 + 3=remainder
and 211/19=11+3(remainder)
here, y=19
so 19/19=1 rem=0.
is it OK?
SVP
Joined: 07 Nov 2007
Posts: 1824
Location: New York
Followers: 29

Kudos [?]: 564 [0], given: 5

Re: mgmat [#permalink]  28 Aug 2008, 19:32
bigtreezl 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?

0
1
2
3
4

x=11y+3
x=19k+3
x= 11*19m+3 =11y+3
11y= 19*11m
y=19m

_________________

Smiling wins more friends than frowning

Intern
Joined: 27 Aug 2007
Posts: 35
Followers: 1

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

Re: mgmat [#permalink]  29 Aug 2008, 21:27
x2suresh wrote:
bigtreezl 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?

0
1
2
3
4

x=11y+3
x=19k+3
x= 11*19m+3 =11y+3
11y= 19*11m
y=19m

Suresh, can you please explain how you wrote the following:
x= 11*19m+3 =11y+3

Thanks.
SVP
Joined: 07 Nov 2007
Posts: 1824
Location: New York
Followers: 29

Kudos [?]: 564 [0], given: 5

Re: mgmat [#permalink]  29 Aug 2008, 21:31
lkothari wrote:
x2suresh wrote:
bigtreezl 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?

0
1
2
3
4

x=11y+3
x=19k+3
x= 11*19m+3 =11y+3
11y= 19*11m
y=19m

Suresh, can you please explain how you wrote the following:
x= 11*19m+3 =11y+3

Thanks.

x=11y+3
x=19k+3
--> 11y=19k here y and k are integers
so y must be multiple of 19
and k must be multipe of 11
11y= 11*19m = 19* 11*n
_________________

Smiling wins more friends than frowning

Re: mgmat   [#permalink] 29 Aug 2008, 21:31
Similar topics Replies Last post
Similar
Topics:
When the integer n is divided by 17, the quotient is x and 3 04 Dec 2007, 19:27
When the positive integer x is divided by 11, the quotient 3 30 Oct 2007, 19:27
When the positive integer x is divided by 11, the quotient 7 31 May 2007, 04:19
What is the remainder when the positive integer x is divided 6 03 Nov 2005, 15:19
What is the remainder when the positive integer x is divided 2 08 Oct 2005, 14:38
Display posts from previous: Sort by