Max@Math Revolution wrote:For a positive integer n, what is the remainder when n(n+1) is divided by 12?
1) n is divisible by 3.
2) n is divisible by 4.
Target question: What is the remainder when n(n+1) is divided by 12?
Statement 1: n is divisible by 3
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 3, in which case n(n+1) = 3(3+1) = 12. Here,
12 divided by 12 leaves remainder 0
Case b: n = 6, in which case n(n+1) = 6(6+1) = 42. Here,
42 divided by 12 leaves remainder 6
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
There are several values of n that satisfy statement 2. Here are two:
Case a: n = 4, in which case n(n+1) = 4(4+1) = 20. Here,
20 divided by 12 leaves remainder 8
Case b: n = 8, in which case n(n+1) = 8(8+1) = 72. Here,
72 divided by 12 leaves remainder 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that n is divisible by 3
Statement 2 tells us that n is divisible by 4
COMBINED, we know that n is divisible by 12.
If n is divisible by 12, then we can be certain that
(n)(n+1) is divisible by 12.
If (n)(n+1) is divisible by 12, then
(n)(n+1) divided by 12 will leave remainder 0
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
