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

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
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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

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