Another remainder...

[alex.gellatly]

What is the remainder when the sum of the positive integers x and y is divided by 6?
1. When x is divided by 6, the remainder is 3.
2. When y is divided by 6, the remainder is 1.

Thanks.

[Birottam Dutta]

You will need both the options to solve this question:

by the first statement, x is of the form 6n+3, where n is any number starting from 0.

So, x can be 3, 9, 15, .... and so on.

But this statement is insufficient because it says nothing about y and we need to find reminder of (x+y)/6.

By statement 2, y is of the form 6m+1, m is again any number starting from 0. So, possible values of y are 1, 7, 13, ... and so on. Again this is insufficient.

Taking both statements together,

(x+y)/6 = {(6n+3) + (6m+1)}/6 = n+m+ 4/6 = n+m+2/3. So, reminder is 2.

Both statements together are sufficient.

[Brent@GMATPrepNow]

What is the remainder when the sum of the positive integers x and y is divided by 6?
1. When x is divided by 6, the remainder is 3.
2. When y is divided by 6, the remainder is 1.

Thanks.

Statement 1: When x is divided by 6, the remainder is 3.
Given this information, we can have several cases that yield different answers to the target question:
case 1: x=3, y=1, which means the remainder is 4, when x+y is divided by 6
case 2: x=3, y=2, which means the remainder is 5, when x+y is divided by 6
NOT SUFFICIENT

Statement 2: When y is divided by 6, the remainder is 1.
Given this information, we can have several cases that yield different answers to the target question:
case 1: x=1, y=1, which means the remainder is 2, when x+y is divided by 6
case 2: x=2, y=1, which means the remainder is 3, when x+y is divided by 6
NOT SUFFICIENT

Statements combined
We have a nice rule that says something like:
If X is the remainder when x is divided by N, and Y is the remainder when y is divided by N, then the remainder when x+y is divided by N is equal to the remainder when X+Y is divided by N (given that x, y, and N are positive integers).

Example: If V divided by 11 leaves remainder 8, and if W divided by 11 leaves remainder 6, then the remainder when V+W is divided by 11 will equal the remainder when 8+6 is divided by 11. In other words, the remainder will be 3.

So, when we combine the two statements, we can see that when x+y is divided by 6 the remainder will be equal to the remainder when 3+1 is divided by 6. In other words, the remainder must be 4.

SUFFICIENT

So, the answer is C

Cheers,
Brent

[GMATGuruNY]

What is the remainder when the sum of the positive integers x and y is divided by 6?
1. When x is divided by 6, the remainder is 3.
2. When y is divided by 6, the remainder is 1.

Thanks.

Clearly neither statement on its own is sufficient.
Statement 1 implies that x = 6a + 3.
Statement 2 implies that y = 6b + 1.
When the statements are combined:
x+y = (6a+3) + (6b+1) = 6(a+b) + 4.
Since the sum of x and y is 4 more than a multiple of 6, when x+y is divided by 6, the remainder will be 4.
SUFFICIENT.

The correct answer is C.