Hi saidov.mikhail,

In this question, we need to know something about both "n" and "s"; to figure out the remainder, we need to know what we're dividing by. Since we're never told anything about "s", there's no way to answer this question.

Fact 1 tells us "n" is odd. Nothing about "s" though.
Fact 1 is INSUFFICIENT.

Fact 2 tells us "n" is greater than 20. Nothing about "s" though.
Fact 2 is INSUFFICIENT.

Combined, we know that "n" is odd AND greater than 20. Still nothing about "s" though.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

saidov.mikhail wrote:If n is a positive integer and r is the remainder when 4+7n is divided by s. What is the value of r?

1) n+1 is divisible by 3
2) n > 20

You might want to go back and edit your original post again. The question should read:

If n is a positive integer and r is the remainder when 4+7n is divided by 3. What is the value of r?

Cheers,
Brent

saidov.mikhail wrote:If n is a positive integer and r is the remainder when 4+7n is divided by 3. What is the value of r?

1) n+1 is divisible by 3
2) n > 20

NOTE: I've edited the question so that it matches the original question.

This question could be worded in a nicer way: If n is a positive integer, what is the remainder when 7n+4 is divided by 3?

Target question: What is the remainder when 7n+4 is divided by 3?

Statement 1: n+1 is divisible by 3
Let's take our target expression (7n+4) and rewrite it as 3(2n+1) + (n+1)
This is useful, because we know that 3(2n+1) is divisible by 3.
Now statement 1 tells us that (n+1) is divisible by 3.
There's a nice rule that says, "If A is divisible by k, and B is divisible by k, then (A+B) is divisible by k."
So, we can conclude that 3(2n+1) + (n+1) is divisible by 3
This means that 7n+4 is divisible by 3
In other words, the remainder is zero when 7n+4 is divided by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > 20
There are several values of n that satisfy this condition. Here are two:
Case a: n = 21, in which case, the remainder is one when 7n+4 is divided by 3
Case b: n = 22, in which case, the remainder is two when 7n+4 is divided by 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent