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# If n is the smallest of three consecutive positive integers, which of

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Joined: 02 Sep 2009
Posts: 59589
If n is the smallest of three consecutive positive integers, which of  [#permalink]

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26 Aug 2018, 06:04
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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

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Re: If n is the smallest of three consecutive positive integers, which of  [#permalink]

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26 Aug 2018, 08:05
Bunuel 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

Product of 3 consecutive positive integers is divisible by 6

$$6 = 3 * 2$$, Thus the Product of 3 consecutive positive integers is divisible by both 2 and 3 , Answer must be (E)
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Re: If n is the smallest of three consecutive positive integers, which of  [#permalink]

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01 Apr 2019, 07:24
Top Contributor
Bunuel 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

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

Cheers,
Brent
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Re: If n is the smallest of three consecutive positive integers, which of  [#permalink]

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03 Apr 2019, 18:00
Bunuel 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

Looking at the answer choices, we see that answer choice E represents the product of 3 consecutive integers, and that product is always divisible by 3! = 6, so it also must be divisible by 3.

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Re: If n is the smallest of three consecutive positive integers, which of   [#permalink] 03 Apr 2019, 18:00
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