OG2015 PS If n is a

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lionsshare: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Aug 09, 2017 3:54 pm

by lionsshare » Sat Sep 16, 2017 1:54 am

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If n is a positive integer, then n(n+1)(n+2) is

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even

OA: E

Can anyone, please explain the solution to this problem. Thanks.

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Source: Beat The GMAT — Problem Solving | Sat Sep 16, 2017 1:54 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 » Sat Sep 16, 2017 6:48 am

lionsshare wrote:If n is a positive integer, then n(n+1)(n+2) is

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even

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
NOTE: the product may be divisible by other numbers as well, but these divisors are guaranteed.

Notice that n, n+1, and n+2 are three consecutive integers.
This means the product of n, n+1, and n+2 will be divisible by 3, 2 and 1
Since n(n+1)(n+2) is divisible by 2, then the product is ALWAYS EVEN.
This means we can eliminate answer choices A and B, because they put restrictions on when the product is even.
We can also eliminate C because it suggests that the product can be odd.
Likewise, since n(n+1)(n+2) is ALWAYS divisible by 3, we can eliminate answer choice D, because it puts a restriction on when the product is divisible by 3

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Sep 16, 2017 10:34 am

Hi lionsshare,

This question can be solved by TESTing VALUES (although you'll need to TEST at least 2 options to properly eliminate all of the wrong answers.

IF...
N = 1, then (N)(N+1)(N+2) = (1)(2)(3) = 6
N = 2, then (N)(N+1)(N+2) = (2)(3)(4) = 24

Answer A is eliminated by the 1st option
Answer B is eliminated by the 2nd option
Answer C is eliminated by the 1st option
Answer D is eliminated by the 2nd option
There's only one option remaining...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Thu Apr 05, 2018 3:10 pm

Building on what Brent said, it helps to recognize that (n)(n + 1)(n + 2) and similar structures are signals of consecutive integers. Here are some other variations on the same pattern:
https://www.beatthegmat.com/is-x-x-2-x- ... 76379.html
https://www.beatthegmat.com/remainders- ... tml#743763
https://www.beatthegmat.com/x-x-1-x-k-t ... tml#770020
https://www.beatthegmat.com/totaly-lost ... tml#716315

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jul 17, 2018 3:45 pm

lionsshare wrote:If n is a positive integer, then n(n+1)(n+2) is

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even

The problem is easiest to solve by substituting numbers for n. We'll try an odd number first and then an even number.

For an odd number, let's let n = 1:

1(1+1)(1+2) = 1(2)(3) = 6

We see that choices A and C can't be the correct choices. Choice A is false because, while the product is even, n is not even. Choice C is false because, while n is odd, the product is even.

For an even number, let's let n = 2:

2(2+1)(2+2) = 2(3)(4) = 24

We see than choices B and D can't be the correct choices. Choice B is false because, while the product is even, n is not odd. Choice D is false because, while the product is divisible by 3, n is even.

Therefore, the only correct answer is choice E. When n is even, the product is indeed divisible by 4.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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