If n is the smallest of three consecutive positive integers

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Mon Apr 01, 2019 3:57 am

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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

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Mon Apr 01, 2019 3:57 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Apr 01, 2019 6:21 am

VJesus12 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
If we 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

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Apr 01, 2019 11:06 am

The product of 3 consecutive positive integers is divisible by 6

$6=3*26=3âˆ—2$, Thus the Product of $3$ consecutive positive integers is divisible by both $2$ and $3$, Answer must be [spoiler](E)[/spoiler]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8149; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 03, 2019 4:58 pm

VJesus12 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

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

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.

Answer: E

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