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how to solve fast: divisibility

This topic has 4 expert replies and 2 member replies
buoyant Master | Next Rank: 500 Posts Default Avatar
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how to solve fast: divisibility

Post Thu Dec 18, 2014 8:08 pm
If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

N is divisible by 3
N is divisible by 7

OA: B

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Zoser Junior | Next Rank: 30 Posts
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16 Jan 2017
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Top Reply
Post Wed Apr 12, 2017 4:17 am
Quote:
Sorry, that should have read "Among a set of consecutive integers, every 3rd integer will be divisible by 3"

This statement is true.
For example: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...
What about:
2,3,4,5,6,7,8,9

4 and 7 are not divisible by "3" eventhough 4 is the 3rd consecutive integer!

Also, in 4,5,6,7,8,9,10,11,12,13 7 is the 4th integer but not divisible by 4!

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Post Wed Apr 12, 2017 4:30 am
Zoser wrote:
Quote:
Sorry, that should have read "Among a set of consecutive integers, every 3rd integer will be divisible by 3"

This statement is true.
For example: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...
What about:
2,3,4,5,6,7,8,9

4 and 7 are not divisible by "3" eventhough 4 is the 3rd consecutive integer!

Also, in 4,5,6,7,8,9,10,11,12,13 7 is the 4th integer but not divisible by 4!
I don't mean to say that, if we have some consecutive integers, the 3rd integer will be divisible by 3, the 6th integer will be divisible by 3, the 9th integer will be divisible by 3, etc.

I means that out of any three consecutive integers, 1 will be divisible by 3.
Likewise, out of any four consecutive integers, 1 will be divisible by 4.
etc

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

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Zoser Junior | Next Rank: 30 Posts
Joined
16 Jan 2017
Posted:
24 messages
Post Wed Apr 12, 2017 4:17 am
Quote:
Sorry, that should have read "Among a set of consecutive integers, every 3rd integer will be divisible by 3"

This statement is true.
For example: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...
What about:
2,3,4,5,6,7,8,9

4 and 7 are not divisible by "3" eventhough 4 is the 3rd consecutive integer!

Also, in 4,5,6,7,8,9,10,11,12,13 7 is the 4th integer but not divisible by 4!

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Post Wed Apr 12, 2017 4:30 am
Zoser wrote:
Quote:
Sorry, that should have read "Among a set of consecutive integers, every 3rd integer will be divisible by 3"

This statement is true.
For example: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...
What about:
2,3,4,5,6,7,8,9

4 and 7 are not divisible by "3" eventhough 4 is the 3rd consecutive integer!

Also, in 4,5,6,7,8,9,10,11,12,13 7 is the 4th integer but not divisible by 4!
I don't mean to say that, if we have some consecutive integers, the 3rd integer will be divisible by 3, the 6th integer will be divisible by 3, the 9th integer will be divisible by 3, etc.

I means that out of any three consecutive integers, 1 will be divisible by 3.
Likewise, out of any four consecutive integers, 1 will be divisible by 4.
etc

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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Post Wed Apr 12, 2017 4:08 am
Zoser wrote:
Quote:
Statement 1: N is divisible by 3
IMPORTANT RULE: Among a set of integers, every 3rd integer will be divisible by 3.
Likewise, every 4th integer will be divisible by 4.
Every 5th integer will be divisible by 5.
Does this rule work all the times?

I tried number 9223 and it is not divisible by 3!

Thanks
Sorry, that should have read "Among a set of consecutive integers, every 3rd integer will be divisible by 3"

This statement is true.
For example: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Zoser Junior | Next Rank: 30 Posts
Joined
16 Jan 2017
Posted:
24 messages
Post Wed Apr 12, 2017 3:20 am
Quote:
Statement 1: N is divisible by 3
IMPORTANT RULE: Among a set of integers, every 3rd integer will be divisible by 3.
Likewise, every 4th integer will be divisible by 4.
Every 5th integer will be divisible by 5.
Does this rule work all the times?

I tried number 9223 and it is not divisible by 3!

Thanks

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