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 Your Progress

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

30 Sep 2012, 16:27

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

58% (00:15) correct 42% (00:17) wrong based on 272 sessions

HideShow timer Statistics

A key ring has 7 keys. How many different ways can they be arranged?

A. 6 B. 7 C. 5! D. 6! E. 7!

I would like to argue against OA. 7 => 6! circular permutations. Therefore, for a keyring - arrangements = 6!/2 (clockwise/anti-clockwise doesn't matter)

Re: A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

01 Oct 2012, 02:18

voodoochild wrote:

A key ring has 7 keys. How many different ways can they be arranged?

a 6 b 7 c 5! d 6! e 7!

I would like to argue against OA. 7 => 6! circular permutations. Therefore, for a keyring - arrangements = 6!/2 (clockwise/anti-clockwise doesn't matter)

Hi voodoochild,

Why wouldn't the direction matter? It's a circular arrangement and you will look at the keyring from one side. Say there are three rings, A, B and C.. .ABC and CBA are two different arrangements, even in a circular arrangement.
_________________

Re: A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

01 Oct 2012, 02:42

3

This post received KUDOS

voodoochild wrote:

A key ring has 7 keys. How many different ways can they be arranged?

a 6 b 7 c 5! d 6! e 7!

I would like to argue against OA. 7 => 6! circular permutations. Therefore, for a keyring - arrangements = 6!/2 (clockwise/anti-clockwise doesn't matter)

Think of choosing one specific key and placing it on the key ring. The remaining 6 keys can now be arranged in 6! ways. Once you have placed one key, you created a row (straighten the circle), so the regular rule for permutations apply. It doesn't matter if you slide the keys clockwise or counter clockwise, they have the same relative position each to the other. For example, just for 3 keys, ABC and ACB are different arrangements. Mirror image arrangements are different, because you don't flip your key ring. At least I think this is what is assumed.

In the case of arrangements around a round table, it is obvious. For sure, you cannot flip your table and the people with it.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

I read this concept while preparing for Indian Engineering entrance examination.... not sure....

Necklace, with spherical beads, can be flipped, so symmetrical arrangements can be considered identical. But, if not explicitly stated, I think you shouldn't assume anything like this.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

01 Dec 2013, 05:52

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: A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

01 Dec 2013, 22:32

This question was ambiguous so I got it wrong. I interpret "keys on a ring" meaning the relative ordering can't change, only moved around the ring. That means either 1 ordering (not an option here), or something where I consider the ordering left-to-right as the keys hang on the ring, but I can move the leftmost key around the loop to put it in the rightmost position, as follows:

Re: A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

16 Oct 2016, 09:51

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: A key ring has 7 keys. How many different ways can they be a [#permalink]

Show Tags

08 Mar 2017, 22:08

voodoochild wrote:

A key ring has 7 keys. How many different ways can they be arranged?

A. 6 B. 7 C. 5! D. 6! E. 7!

I would like to argue against OA. 7 => 6! circular permutations. Therefore, for a keyring - arrangements = 6!/2 (clockwise/anti-clockwise doesn't matter)

In a permutations problem that involves a circular arrangement (such as keys on a ring, or people seated around a circular table), the number of permutations is equal to (N - 1)!. This is because there is no beginning or end to the ring (or no left end or right end). Consider the three-item arrangement of A, B, C. In a row, ABC is different from BCA, but if they're in a circle they're the same arrangement: B is between A and C, A is between C and B, etc.

So in this problem, with 7 keys, the calculation is (7 - 1)!, which is 6! which equals 720.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."