BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If n is the smallest of three consecutive positive integers, which of the following must be true?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

If n is the smallest of three consecutive positive integers, which of the following must be true?

by BTGmoderatorDC » Tue Dec 01, 2020 6:02 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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


OA E

Source: Manhattan Prep
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Re: If n is the smallest of three consecutive positive integers, which of the following must be true?

by Brent@GMATPrepNow » Wed Dec 02, 2020 9:22 am
BTGmoderatorDC wrote: ↑
Tue Dec 01, 2020 6:02 pm
 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


OA E

Source: Manhattan Prep
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

Re: If n is the smallest of three consecutive positive integers, which of the following must be true?

by swerve » Thu Dec 03, 2020 10:51 am
BTGmoderatorDC wrote: ↑
Tue Dec 01, 2020 6:02 pm
 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


OA E

Source: Manhattan Prep
The product of \(3\) consecutive positive integers is divisible by \(6\)

\(6=3\cdot 2\), Thus the product of \(3\) consecutive positive integers is divisible by both \(2\) and \(3\).

Therefore, E
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: If n is the smallest of three consecutive positive integers, which of the following must be true?

by Scott@TargetTestPrep » Sat Dec 05, 2020 6:04 pm
BTGmoderatorDC wrote: ↑
Tue Dec 01, 2020 6:02 pm
 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


OA E

Solution:

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1