BTGmoderatorDC wrote:If n is an integer greater than 6, which of the following must be divisible by 3 ?
(A) n(n + 1)(n - 4)
(B) n(n + 2)(n - 1)
(C) n(n + 3)(n - 5)
(D) n(n + 4)(n - 2)
(E) n(n + 5)(n - 6)
OA A
Source: Official Guide
We can let n = 7 and then analyze each answer choice:
A) 7(8)(3) is divisible by 3.
B) 7(9)(6) is divisible by 3.
C) 7(10)(2) is not divisible by 3.
D) 7(11)(5) is not divisible by 3.
E) 7(12)(1) is divisible by 3.
We can eliminate choices C and D.
Now let n = 8 and analyze the remaining 3 choices:
A) 8(9)(4) is divisible by 3.
B) 8(10)(7) is not divisible by 3.
E) 8(13)(2) is not divisible by 3.
We see that the correct choice must be A.
Alternate Solution:
Let's analyze each answer choice:
A) If n is divisible by 3, then the product n(n + 1)(n - 4) is also divisible by 3. If n produces a remainder of 1 when divided by 3 (for example, n = 7), then n - 4 must be divisible by 3. Finally, if n produces a remainder of 2 when divided by 3, n + 1 is divisible by 3. In either case, we see that the product has a factor that is a multiple of 3; therefore the product is always divisible by 3.
Answer: A
