GRE Prep 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
Track
Your Progress
Practice
Pays
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
[#permalink]
25 Aug 2018, 00:11
25 Aug 2018, 00:11
00:00
Question Stats:
86% (00:48) correct
13% (01:14) wrong based on 22 sessions
Hide Show 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
Source: Manhattan 5lb
(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
Source: Manhattan 5lb
Re: Number System
[#permalink]
25 Aug 2018, 00:30
25 Aug 2018, 00:30
Expert Reply
The simplest way to go about this is to write this out. Assume two sets of numbers and check each option. The correct option would hold true for all such series.
Case 1: 3, 4, 5
Case 2: 4, 5, 6
Hence only option E holds in both cases.
Case 1: 3, 4, 5
Case 2: 4, 5, 6
| Options | 3, 4, 5 | 4, 5, 6 |
| n is divisible by 3 | true | False |
| n is even | False | True |
| n is odd | True | False |
| (n)(n + 2) is even | False | True |
| n(n + 1)(n + 2) is divisible by 3 | True | True |
Hence only option E holds in both cases.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If n is the smallest of three consecutive positive integers
[#permalink]
02 Dec 2020, 09:22
02 Dec 2020, 09:22
1
Shrija Roy 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
Source: Manhattan 5lb
(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
Source: Manhattan 5lb
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
