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25 Nov 2021, 14:12
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gregspirited
For this question, we can quickly test values to eliminate answer choices.
For example, let's test \(n = 1\)
Wait a second. Why am I testing \(n = 1\), when the question clearly tells us that \(n\) is greater than 6?
In my opinion, the test makers added that proviso (n > 6) so that students don't have to know whether 0 is divisible by 3.
What really matters here is that all integers fall into three categories when it comes to divisibility by 3:
- the number is divisible by 3
- the number leaves a remainder of 1 when divided by 3
- the number leaves a remainder of 2 when divided by 3
The first number I'm testing (\(n = 1\)) leaves a remainder of 1 when divided by 3. As you'll see, when I plug that value into answer choice A, the result is divisible by 3. You'll find that if you take ANY integer that leaves a remainder of 1 when divided by 3 and plug it in to answer choice A, the result will always be divisible by 3.
So, rather than test large values of n, I'm going to save some time and test small values (even though I'm breaking the restriction that n > 6)
A. \(1 (1+1) (1-4)=-6\) Divisible by 3
B. \(1 (1+2) (1-1)=0\) Divisible by 3
C. \(1 (1+3) (1-5)=-16\) NOT divisible by 3. Eliminate.
D. \(1 (1+4) (1-2)=-5\) NOT divisible by 3. Eliminate.
E. \(1 (1+5) (1-6)=-30\) Divisible by 3
Now let's test \(n = 2\)
A. \(2 (2+1) (2-4)=-12\) Divisible by 3
B. \(2 (2+2) (2-1)=8\) NOT divisible by 3. Eliminate.
E. \(2 (2+5) (2-6)=-56\) NOT divisible by 3. Eliminate.
Answer: A
13 Apr 2022, 17:53
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carcass
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
26 Nov 2022, 12:45
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BrentGMATPrepNow
Hi BrentGMATPrepNow, for answer choice A : (A) 7(7 + 1)(7 – 4) = (7)(8)(3) = 7+8+3 = 21/3 Divisible by 3 so correct answer choice.
Is this way of calculation is correct? Thanks Brent
