Remainder when divided by 3

[Brent@GMATPrepNow]

What is remainder when x^2 - 4x + 11 is divided by 3
(1) x+1 is divisible by 3
(2) x-2 is divisible by 3

[720dreaming]

I'll go with D.

A) Since (x+1) is divisible by 3, we know that (X+1)(X-5) is divisible by 3. This gives us x^2-4x-5. This is divisible by 3. To get the equation in the question we need to add 16. Since 15 is divisble by 3, the R=1. Sufficient.

B)Similar logic to above. (x-2)(x-2) is divisible by 3. X^2-4x+4 is divisible by 3. We need to add 7 to get the original equation. Since 6 is divisible by 3, R=1.

[Brent@GMATPrepNow]

Nice work, 720Dreaming.
The answer is D.

Here's my full solution as well:
(1) one option is to plug in 2 values (or 3 to provide a little more certainty) for x such that x+1 is divisible by 3 (e.g., x=2, 5, 8 etc) and check whether each value of x yields the same remainder when x^2 - 4x + 11 is divided by 3
(2) Recognize that this information is the same information that was provided in (1). If x+1 is divisible by 3, then it must follow that x-2 is divisible by 3.
When (1) and (2) provide identical information, then the correct answer must be either D or E.
Let's see when the correct answer is D.
When we look at the expression x^2 - 4x + 11, we can see that it’s ALMOST possible to factor out x-2 from this expression. In fact (x-2)^2 = x^2 + 4x + 4
So, we can rewrite x^2 - 4x + 11 as x^2 + 4x + 4 +7, which is the same as (x-2)^2 +7, which is the same as (x-2)^2 +6 + 1
Since x-2 is divisible by 3, it must be true that (x-2)^2 is divisible by 3 and it follows that (x-2)^2 +6 is divisible by 3
So, (x-2)^2 +6 + 1 (aka x^2 - 4x + 11) must have a remainder of 1 when divided by 3

[logitech]

(1) x+1 is divisible by 3

x+1 = 3

x=2, R=1

(2) x-2 is divisible by 3

x-2=3

x=5, R=1

D