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
