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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Aug 27, 2020 12:06 pm

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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

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Source: Beat The GMAT — Problem Solving | Thu Aug 27, 2020 12:06 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; 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 » Thu Aug 27, 2020 4:35 pm

BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:06 pm
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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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 » Mon Aug 31, 2020 10:31 am

BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:06 pm
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: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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