GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 03:18 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If n is the smallest of three consecutive positive integers, which of

Author Message
TAGS:

### Hide Tags

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

### Show Tags 00:00

Difficulty:   5% (low)

Question Stats: 85% (00:54) correct 15% (00:57) wrong based on 97 sessions

### HideShow timer Statistics

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

_________________
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4834
Location: India
GPA: 3.5
Re: If n is the smallest of three consecutive positive integers, which of  [#permalink]

### Show Tags

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)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: If n is the smallest of three consecutive positive integers, which of  [#permalink]

### Show Tags

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
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: If n is the smallest of three consecutive positive integers, which of  [#permalink]

### Show Tags

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If n is the smallest of three consecutive positive integers, which of   [#permalink] 03 Apr 2019, 18:00
Display posts from previous: Sort by

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