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

 It is currently 17 Oct 2019, 01:00 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.  Are i, j, k consecutive integers?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Director  Joined: 07 Jun 2004
Posts: 556
Location: PA
Are i, j, k consecutive integers?  [#permalink]

Show Tags

4 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:36) correct 30% (01:43) wrong based on 275 sessions

HideShow timer Statistics

Are i, j, k consecutive integers?

(1) The remainder when i + j + k is divided by 3 is 2
(2) The remainder when i*j*k is divided by 3 is 1
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Consecutive integers  [#permalink]

Show Tags

2
8
rxs0005 wrote:
Are i , j , k consecutive integers

The remainder when i + j + k is divided by 3 is 2

The remainder when i*j*k is divided by 3 is 1

I think it's meant that $$i$$, $$j$$, and $$k$$ are integers.

NOTES:
Out of any 3 consecutive integers exactly one is divisible by 3. So the product of ANY 3 consecutive integers is divisible by 3 (so remainder is zero).

Consecutive integers can be represented as ... $$n-1$$, $$n$$, $$n+1$$, ... where $$n$$ is an integer. Sum of 3 consecutive integers would be $$(n-1)+n+(n+1)=3n$$, so the sum of ANY 3 consecutive integers is divisible by 3 (so remainder is zero).

More generally:
• If $$k$$ is odd, the sum of $$k$$ consecutive integers is always divisible by $$k$$. Given $$\{9,10,11\}$$, we have $$k=3$$ consecutive integers. The sum of 9+10+11=30, therefore, is divisible by 3.

• If $$k$$ is even, the sum of $$k$$ consecutive integers is never divisible by $$k$$. Given $$\{9,10,11,12\}$$, we have $$k=4$$ consecutive integers. The sum of 9+10+11+12=42, therefore, is not divisible by 4.

• The product of $$k$$ consecutive integers is always divisible by $$k!$$, so by $$k$$ too. Given $$k=4$$ consecutive integers: $$\{3,4,5,6\}$$. The product of 3*4*5*6 is 360, which is divisible by 4!=24.

(1) The remainder when i + j + k is divided by 3 is 2 --> as the remainders is not zero, then $$i$$, $$j$$, and $$k$$ are not consecutive integers. Sufficient.

(2) The remainder when i*j*k is divided by 3 is 1--> as the remainders is not zero, then $$i$$, $$j$$, and $$k$$ are not consecutive integers. Sufficient.

Hope it helps.
_________________
General Discussion
Current Student D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: Are i, j, k consecutive integers?  [#permalink]

Show Tags

Excellent Question.
Here is what i did in this one =>

RULE -> Sum and Product of 3 consecutive integers is always divisible by 3.

Statement 1=>
Sum =3k+2 => They can never be consecutive
Statement 2=>
Product =3k+1
Hence they can never be consecutive.

Hence D

_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13204
Re: Are i, j, k consecutive integers?  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Are i, j, k consecutive integers?   [#permalink] 21 Dec 2018, 05:42
Display posts from previous: Sort by

Are i, j, k consecutive integers?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  