alex.gellatly wrote: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
