Problem Solving

What is the remainder when the positive integer x is divided by 3?

(1) when x is divided by 6, the remainder is 2.
(2) when x is divided by 15, the remainder is 2.

Target question: What is the remainder when the positive integer x is divided by 3?

IMPORTANT CONCEPT: Notice that 3 is a factor of 6 and 15. So, if some integer k is a multiple of 6, then k is also a multiple of 3. For example, since 102 is a multiple of 6, then 102 must also be a multiple of 3. Likewise, if some integer k is a multiple of 15, then k is also a multiple of 3.

Statement 1: when x is divided by 6, the remainder is 2
In other words, x is 2 greater than some multiple of 6. (e.g., x = 2, 8, 14, 20, etc)
Applying the green concept above, we can also say that x is 2 greater than some multiple of 3.
If x is 2 greater than some multiple of 3, then the remainder must be 2 when x is divided by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: when x is divided by 15, the remainder is 2
In other words, x is 2 greater than some multiple of 15. (e.g., x = 2, 17, 32, etc)
Applying the green concept above, we can also say that x is 2 greater than some multiple of 3.
If x is 2 greater than some multiple of 3, then the remainder must be 2 when x is divided by 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Elena Plescan wrote:Brent,

Thank you a lot. The number in the example was 15, not 12, but I guess that doesn't change the answer at all.
Thanks again,
Elena

Oops.
You're right, though. The same concepts still apply.
That said, I've edited my response.

Cheers,
Brent