BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remain

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1223
Joined: Sat Feb 15, 2020 2:23 pm
Followed by:1 members

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remain

by BTGModeratorVI » Mon Jun 08, 2020 11:59 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

Answer: A
Source: Manhattan prep
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

Re: When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the re

by Jay@ManhattanReview » Mon Jun 08, 2020 10:03 pm
BTGModeratorVI wrote: ↑
Mon Jun 08, 2020 11:59 am
 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

Answer: A
Source: Manhattan prep
Given the information, we have x = 11y + 3.

Also, x = 19q + 3; where q = quetient

=> 11y + 3 = 19q + 3

11y = 19q

Since y and q are positive integers and co-prime, we have y = multiple of 19 and q = multiple of 11

Say y = 19, then 19 divided by 19 has a remainder 0.

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Classes | GMAT Tutoring | GRE Tutoring | LSAT Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Re: When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the re

by Brent@GMATPrepNow » Tue Jun 09, 2020 5:03 am
BTGModeratorVI wrote: ↑
Mon Jun 08, 2020 11:59 am
 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

Answer: A
Source: Manhattan prep
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

Answer: A
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Junior | Next Rank: 30 Posts
Posts: 11
Joined: Sat May 30, 2020 5:24 am

Re: When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the re

by i256 » Tue Jun 09, 2020 9:53 am
Now, write the equations down, x= 11 y + 3
, and x = 19 t + 3

11y = 19t

y= 19 t/11 , y has to be divisible by 19

Hence, the remainder is 0
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8083
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the re

by Scott@TargetTestPrep » Wed Jun 10, 2020 1:01 pm
BTGModeratorVI wrote: ↑
Mon Jun 08, 2020 11:59 am
 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

Answer: A
Solution:

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: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1