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If n is the smallest of three consecutive positive integers

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If n is the smallest of three consecutive positive integers [#permalink] New post 25 Aug 2018, 00:11
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Question Stats:

80% (00:50) correct 20% (00:36) wrong based on 10 sessions
If n is the smallest of three consecutive positive integers, which of the following must be true?


(A) n is divisible by 3

(B) n is even

(C) n is odd

(D) (n)(n + 2) is even

(E) n(n + 1)(n + 2) is divisible by 3


Source: Manhattan 5lb
[Reveal] Spoiler: OA
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Re: Number System [#permalink] New post 25 Aug 2018, 00:30
Expert's post
The simplest way to go about this is to write this out. Assume two sets of numbers and check each option. The correct option would hold true for all such series.

Case 1: 3, 4, 5

Case 2: 4, 5, 6

Options3, 4, 54, 5, 6
n is divisible by 3trueFalse
n is evenFalseTrue
n is oddTrueFalse
(n)(n + 2) is evenFalseTrue
n(n + 1)(n + 2) is divisible by 3TrueTrue


Hence only option E holds in both cases.
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Re: If n is the smallest of three consecutive positive integers [#permalink] New post 02 Dec 2020, 09:22
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Expert's post
Shrija Roy wrote:
If n is the smallest of three consecutive positive integers, which of the following must be true?


(A) n is divisible by 3

(B) n is even

(C) n is odd

(D) (n)(n + 2) is even

(E) n(n + 1)(n + 2) is divisible by 3


Source: Manhattan 5lb


There's a nice rule says:
The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1
So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1
Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, 2 and 1

By the above rule, the product of 3 consecutive integers will be divisible by 3, 2 and 1
Now recognize that n, n+1 and n+2 represent 3 consecutive integers
So, n(n + 1)(n + 2) must be divisible by 3

Answer: E

Cheers,
Brent
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Re: If n is the smallest of three consecutive positive integers   [#permalink] 02 Dec 2020, 09:22
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