NEW HERE? LEARN MORE
closeclose
Last visit was: 09 May 2024, 17:29 It is currently 09 May 2024, 17:29
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Suppose n children are going to sit, in any order, on a row of n chair

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93124
Own Kudos [?]: 622485 [38]
Given Kudos: 81810
Send PM
CAT Tests Forum Quiz Mode
Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   23 Feb 2015, 03:24
10
Kudos
28
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

76% (01:09) correct 24% (01:24) wrong based on 1051 sessions
Hide Show timer Statistics
Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n?

(1) In this row, there are 5040 possible arrangements of the n children.
(2) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children.
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93124
Own Kudos [?]: 622485 [13]
Given Kudos: 81810
Send PM
CAT Tests Forum Quiz Mode
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   02 Mar 2015, 06:51
7
Kudos
6
Bookmarks
Expert Reply
Bunuel wrote:
Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n?

(1) In this row, there are 5040 possible arrangements of the n children.
(2) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children.


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

This is a question about permutations. Because this is Data Sufficiency, we don’t have to bother with the details of calculating n! —- it’s enough to know that if we know the value of n, we can figure out the value of n!, and vice versa!

Statement #1: this gives us n! = 5040 — from this we could figure out n. Statement #1, alone and by itself, is sufficient.

Statement #2: this tells us, essentially, n! – (n – 1)! = 4320. Well, if we went through list of factorials, there could be only one pair that is separated by exactly 4320. We don’t have to know what it is — it’s enough to know that this fact determines a unique value of n. Statement #2, alone and by itself, is sufficient.

Answer = D.

(BTW, n = 7 if you’re curious!)
General Discussion
avatar
B
Psiva00734
Manager
Manager
Joined: 19 Jan 2015
Status:single
Posts: 65
Own Kudos [?]: 66 [1]
Given Kudos: 1169
Location: India
GPA: 3.2
WE:Sales (Pharmaceuticals and Biotech)
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   23 Feb 2015, 03:40
1
Kudos
statement 1
If n children sits in nchairs then arrangements is n!

Total arrangements is 5040. it equals to 7!.

It is sufficient.

Statement 2
By removing one children from n is( n-1) and one chair from n row is( n-1) than arrangements is n! - (n-1)!.
Arrangement is 4320 left. it means 7! - 6!.
5040 - 720= 4320.
It is also sufficient.

so answer is D
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11676 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   04 Mar 2015, 23:56
Expert Reply
Hi All,

There are going to be a few questions on Test Day that require the use of factorials. While it's not necessary to have these calculations memorized, if you DO have them memorized, then you'll likely be able to move much faster on these handful of questions.

2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040

You're not likely to have to deal with much higher than 7! as a 'solo' calculation. In a question such as this one, this knowledge can help you to quickly work through the prompt.

GMAT assassins aren't born, they're made,
Rich
User avatar
S
TheKingInTheNorth
Manager
Manager
Joined: 13 Mar 2013
Posts: 135
Own Kudos [?]: 288 [0]
Given Kudos: 25
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE:Engineering (Telecommunications)
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   10 Sep 2015, 07:17
Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n?

(1) In this row, there are 5040 possible arrangements of the n children.
(2) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children.

Statement 1 . Sufficient
because n children can be arranged in n chairs in n! ( n factorials ways )
and 7! =5040

Statement : 2 Sufficient
Because 7! = 5040
and if we remove one person and one chair then there would be 4320 scenario .

6!=720
7! - 6! = 4320
avatar
B
mynguyen62
Intern
Intern
Joined: 26 Jan 2017
Posts: 6
Own Kudos [?]: 1 [0]
Given Kudos: 2
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   17 May 2017, 10:24
Sorry if I'm asking naive questions but all of the above members have no difficulties in pointing out that 7! = 5040, so that they could easily reach the answer.

To me, 5040 seems alien. I can't tell 5040 is a factorial at a glance.

Okay, I see someone recommending that it is useful to memorize the factorials from 1! to 7!. That may be the method to solve this particular question.

But what if the question gives random numbers, which we don't know for sure if they are factorials or not? For example, statement (1): n! = 12345, statement (2): n! - (n-1)! = 1234.

Thanks for any help,
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11676 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   17 May 2017, 13:18
2
Kudos
Expert Reply
mynguyen62 wrote:
Sorry if I'm asking naive questions but all of the above members have no difficulties in pointing out that 7! = 5040, so that they could easily reach the answer.

To me, 5040 seems alien. I can't tell 5040 is a factorial at a glance.

Okay, I see someone recommending that it is useful to memorize the factorials from 1! to 7!. That may be the method to solve this particular question.

But what if the question gives random numbers, which we don't know for sure if they are factorials or not? For example, statement (1): n! = 12345, statement (2): n! - (n-1)! = 1234.

Thanks for any help,


Hi mynguyen62,

As a subject, factorials are relatively rare on the GMAT (you'll likely see just one question on the subject on Test Day). That having been said, nothing about factorials is "random", so there cannot be a Quant question involving factorials that uses random numbers. As such, if you're told that N! = a specific number, then there is just ONE possible value for N (and the same can be said for the difference between two Factorials). Knowing that 7! = 5040 might make it easier to 'process' the information in this question, but it's not necessary to know that IF you realize that a different "N" leads to a different/unique result for N!

GMAT assassins aren't born, they're made,
Rich
avatar
B
Sachin07
Intern
Intern
Joined: 07 Jan 2017
Posts: 14
Own Kudos [?]: 14 [1]
Given Kudos: 21
Location: India
Concentration: Other, Other
Schools: UConn"19
WE:Medicine and Health (Pharmaceuticals and Biotech)
Send PM
Reviews Badge
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 Jun 2017, 13:30
1
Kudos
Statement 1 . Sufficient
there are 5040 possible arrangements of the n children And because n children can be arranged in n chairs in n!
thus n!=5040
Using prime factorisation I found n=7

Statement : 2 Sufficient
and if we remove one person and one chair then there would be 4320 scenario
n!-(n- 1)!=4320
Taking (n-1) common , (n-1).(n-1)!=4320
Using prime factorisation u can find (n-1) to be 6
6*6! = 4320

And D
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1904
Own Kudos [?]: 5612 [0]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 May 2018, 07:17
Expert Reply
Bunuel, chetan2u, EMPOWERgmatRichC, VeritasPrepKarishma

if \(n!-(n-1)!\) = K (a constant integer)

Can the value of n be uniquely determined ?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65206 [1]
Given Kudos: 431
Location: Pune, India
Send PM
Forum Quiz Mode
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 May 2018, 09:33
1
Kudos
Expert Reply
gmatbusters wrote:
Bunuel, chetan2u, EMPOWERgmatRichC, VeritasPrepKarishma

if \(n!-(n-1)!\) = K (a constant integer)

Can the value of n be uniquely determined ?


Note the pattern:
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720

The difference between consecutive factorials keeps increasing (obviously since every time you are multiplying it by the next greater number).
So there will be only one pair of consecutive values for any given constant.

Say K = 18. Then n = 4
Say K = 600. Then n = 6
and so on...
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1904
Own Kudos [?]: 5612 [1]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 May 2018, 10:02
1
Kudos
Expert Reply
Thank you for giving insights...

VeritasPrepKarishma wrote:

if \(n!-(n-1)!\) = K (a constant integer)

Can the value of n be uniquely determined ?


Note the pattern:
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720

The difference between consecutive factorials keeps increasing (obviously since every time you are multiplying it by the next greater number).
So there will be only one pair of consecutive values for any given constant.

Say K = 18. Then n = 4
Say K = 600. Then n = 6
and so on...[/quote]
avatar
S
ColumbiaEMBA
Manager
Manager
Joined: 29 Sep 2017
Posts: 89
Own Kudos [?]: 60 [1]
Given Kudos: 10
Location: United States
Send PM
GMAT ToolKit User Reviews Badge
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 May 2018, 14:21
1
Kudos
Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n?

(1) In this row, there are 5040 possible arrangements of the n children.
(2) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children.

1) Would GMAT give 5041 as an answer? Nope, never seen it. Given it's a straight number, this will be sufficient.
2) Same logic applies. Would the difference of n! - (n-1)! be some random number? Nope; thus, this will be sufficient.

Without solving, I would wager on D.
avatar
B
BeePen
Intern
Intern
Joined: 14 May 2018
Posts: 10
Own Kudos [?]: 0 [0]
Given Kudos: 17
Schools: Stern '21 (A)
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 May 2018, 14:30
Explain u posted is helpful ! but do not understand why B can be right ? How can u calculate on exam with no calc?
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1904
Own Kudos [?]: 5612 [0]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   14 May 2018, 18:17
Expert Reply
BeePen, please see the below explanation by veritasprepkarishma

if \(n!-(n-1)!\) = K (a constant integer), n can be uniquely found




Note the pattern:
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720

The difference between consecutive factorials keeps increasing (obviously since every time you are multiplying it by the next greater number).

So there will be only one pair of consecutive values for any given constant.

Say K = 18. Then n = 4
Say K = 600. Then n = 6
and so on...[/quote]
User avatar
L
adkikani
IIM School Moderator
Joined: 04 Sep 2016
Posts: 1261
Own Kudos [?]: 1242 [0]
Given Kudos: 1207
Location: India
WE:Engineering (Other)
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   18 Jul 2018, 00:01
Bunuel niks18 chetan2u pushpitkc

Quote:
Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n?

(2) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children.



Can you please explain St 2: How we interpret : n! – (n – 1)! = 4320
when we have same no of children and chair and start and now we removed each of one chair and one children.
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5216 [3]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   18 Jul 2018, 03:14
2
Kudos
1
Bookmarks
adkikani wrote:
Bunuel niks18 chetan2u pushpitkc

Quote:
Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n?

(2) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children.



Can you please explain St 2: How we interpret: n! – (n – 1)! = 4320
when we have same no of children and chair and start and now we removed each of one chair and one children.


Hi adkikani

The 'n' children can be arranged in 'n' chairs is n! ways
After 1 chair is removed, the 'n-1' children can be arranged in (n-1)! ways

Statement 2 says that if one child leaves and one chair is removed

To understand this clearly, let's consider n = 3.

So, how can we seat 3 children in 3 chairs -
3 ways of seating one of the 3 children in the first chair
2 ways of seating one of the 2 children in the second chair
1 ways of seating one child in the third chair (3*2*1), which is 3!

Similarly, we can seat 2 children in 2 chairs as (2*1), which is 2!

Therefore, the total number of ways must be n! - (n-1)!

Hope this helps you!
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4129
Own Kudos [?]: 9268 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   18 Sep 2020, 06:19
Expert Reply
GMATBusters wrote:
if \(n!-(n-1)!\) = K (a constant integer)

Can the value of n be uniquely determined ?


Yes. If you first look at, say, 8!- 7!, you can factor out the "7!"

8! - 7! = (8)(7!) - 7! = (7!)(8 - 1) = (7)(7!)

and similarly, you can factor (n-1)! from n! - (n-1)!

n! - (n-1)! = (n)(n-1)! - (n-1)! = (n-1)! (n - 1)

Notice the larger n is, the larger (n-1)! (n-1) will be, so if you know it equals some fixed value K, there can only be one value of n that could work.

mynguyen62 wrote:
Okay, I see someone recommending that it is useful to memorize the factorials from 1! to 7!. That may be the method to solve this particular question.


I'd be curious if anyone can point to a single official problem where it would be useful to have memorized the value of 7! in advance. I can't imagine an official GMAT question where that would be helpful.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32889
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink] New post   22 Apr 2024, 00:17
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.
GMAT Club Bot
gmatclubot
Re: Suppose n children are going to sit, in any order, on a row of n chair [#permalink]
22 Apr 2024, 00:17
Moderator:
Bunuel
Math Expert
93124 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions