carcass 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)
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test possible values of n until we eliminate four of the five answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also apply some divisibility properties, but I'm not necessarily sure it will be any faster.
So I'll start testing possible n-values The only condition placed on the value of n is that it must be an integer greater than 6.
So let's start by plugging
n = 7 into the five answer choices:
(A)
7(
7 + 1)(
7 – 4) = (7)(8)(
3), which is clearly divisible by 3. KEEP.
(B)
7(
7 + 2)(
7 – 1) = (7)(
9)(6), which is clearly divisible by 3. KEEP.
(C)
7(
7 + 3)(
7 – 5) = (7)(10)(2), which is NOT divisible by 3. Eliminate.
(D)
7(
7 + 4)(
7 – 2) = (7)(11)(5), which is NOT divisible by 3. Eliminate.
(E)
7(
7 + 5)(
7 – 6) = (7)(
12)(1), which is clearly divisible by 3. KEEP.
We're down to choices A, B and E.Now let's plug
n = 8 into the three remaining answer choices:
(A)
8(
8 + 1)(
8 – 4) = (8)(
9)(4), which is clearly divisible by 3. KEEP.
(B)
8(
8 + 2)(
8 – 1) = (8)(10)(7), which is NOT divisible by 3. Eliminate.
(E)
8(
8 + 5)(
8 – 6) = (8)(13)(2), which is NOT divisible by 3. Eliminate.
By the process of elimination, the correct answer is A