MBA Spotlight Fair Join 40 AdComs at Virtual MBA + Masters Fair! Register to Reserve Your Spot | See Schedule | Win Prizes
close
It is currently 30 Nov 2021, 16:02
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

MBA Spotlight – Top 40 MBA Fair
Nov 29 - Dec 1, 2021

Register Schedule
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
How many words can be formed using all the letters of "EQUAT
10 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
B
cyberjadugar
Senior Manager
Senior Manager
Joined: 28 Mar 2012
Posts: 279
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
How many words can be formed using all the letters of "EQUAT [#permalink] New post  16 Jun 2012, 19:38
21
Bookmarks
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

56% (01:26) correct 44% (01:51) wrong based on 245 sessions

Hide Show timer Statistics

How many words can be formed using all the letters of "EQUATION" such that A always comes after Q (not necessarily together)?

A. 7!
B. 2*7!
C. 4*7!
D. 8!/3
E. 8!/6

This question is created by me, I couldn't find similar question in the forum:
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Expert Reply
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 82990
Premium Member CAT Tests Forum Quiz Mode Top Member of the Month
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  17 Jun 2012, 01:21
4
Kudos
4
Bookmarks
Expert Reply
cyberjadugar wrote:
How many words can be formed using all the letters of "EQUATION" such that A always comes after Q (not necessarily together)?

A. 7!
B. 2*7!
C. 4*7!
D. 8!/3
E. 8!/6

This question is created by me, I couldn't find similar question in the forum:


Responding to a pm.

Since there are 8 distinct letters in the word EQUATION, then the # of arrangements of these letters would be 8!. Now, in half of these cases A will be after Q and in half of these cases Q will be after A.

Therefore the final answer is \(\frac{8!}{2}=\frac{7!*8}{2}=4*7!\).

Answer: C.

Questions about the same concept to practice:
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html

Hope it helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
gmatdog
Intern
Intern
Joined: 03 Jun 2012
Posts: 23
Location: United States
WE:Project Management (Computer Software)
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  16 Jun 2012, 20:38
2
Kudos
1
Bookmarks
Answer C.

There are 8 unique alphabets, so 8! ways of arranging them.

For the restriction of A coming after Q -
Among all possible arrangements, in half of the cases A will be before Q - and in the other half it will be after Q.

So answer = 8! / 2 = 8 / 2 x 7! = 4 x 7!
User avatar
B
cyberjadugar
Senior Manager
Senior Manager
Joined: 28 Mar 2012
Posts: 279
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  17 Jun 2012, 01:27
Bunuel wrote:
Questions about the same concept to practice:
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html

Hi,

These are some awesomely worded questions. :-D

Regards,
avatar
sanjoo
Senior Manager
Senior Manager
Joined: 06 Aug 2011
Posts: 292
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  17 Jun 2012, 02:48
1
Kudos
how can we knw that there will be half times A will cum after Q and Q after A???

m confused ..!!
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Signature Read More
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 82990
Premium Member CAT Tests Forum Quiz Mode Top Member of the Month
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  17 Jun 2012, 02:51
Expert Reply
sanjoo wrote:
how can we knw that there will be half times A will cum after Q and Q after A???

m confused ..!!


Ask yourself: why should any of these two orderings have preferences over the other. Does probability favor one ordering over another?

Follow the links in my previous posts to practice more questions about this concept.

Hope it helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
S
sach24x7
Manager
Manager
Joined: 15 Aug 2014
Status:Don't Give Up!
Posts: 83
Location: India
Concentration: Operations, General Management
Schools: INSEAD Jan '20, HEC Jan20 Intake, IE, IIMA PGPX"20, IIMB EPGP"20
GMAT Date: 04-25-2015
WE:Engineering (Manufacturing)
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  29 Oct 2014, 01:45
Bunuel wrote:
cyberjadugar wrote:
How many words can be formed using all the letters of "EQUATION" such that A always comes after Q (not necessarily together)?

A. 7!
B. 2*7!
C. 4*7!
D. 8!/3
E. 8!/6

This question is created by me, I couldn't find similar question in the forum:


Responding to a pm.

Since there are 8 distinct letters in the word EQUATION, then the # of arrangements of these letters would be 8!. Now, in half of these cases A will be after Q and in half of these cases Q will be after A.

Therefore the final answer is \(\frac{8!}{2}=\frac{7!*8}{2}=4*7!\).

Answer: C.

Questions about the same concept to practice:
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html

Hope it helps.


Are there any restrictions while using this approach? Can you please explain?
User avatar
B
cyberjadugar
Senior Manager
Senior Manager
Joined: 28 Mar 2012
Posts: 279
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  29 Oct 2014, 03:09
1
Kudos
sach24x7 wrote:
Bunuel wrote:
cyberjadugar wrote:
How many words can be formed using all the letters of "EQUATION" such that A always comes after Q (not necessarily together)?

A. 7!
B. 2*7!
C. 4*7!
D. 8!/3
E. 8!/6

This question is created by me, I couldn't find similar question in the forum:


Responding to a pm.

Since there are 8 distinct letters in the word EQUATION, then the # of arrangements of these letters would be 8!. Now, in half of these cases A will be after Q and in half of these cases Q will be after A.
Therefore the final answer is \(\frac{8!}{2}=\frac{7!*8}{2}=4*7!\).
Answer: C.
Questions about the same concept to practice:
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html
Hope it helps.

Are there any restrictions while using this approach? Can you please explain?


Hi,

The only restriction that you should keep in mind is that how the arrangements are made. In this question, sequence of two alphabets is mentioned. Further extrapolation can be made for three alphabets. For E comes after Q, and Q comes after U, required cases would be 1/6 of total arrangements.
E,Q and U can be arranged in 3! or 6 ways. While the sequence EQU in that order will occur only once.

Hope it helps.

Regards,
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2302
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  10 Apr 2016, 18:30
cyberjadugar wrote:
How many words can be formed using all the letters of "EQUATION" such that A always comes after Q (not necessarily together)?

A. 7!
B. 2*7!
C. 4*7!
D. 8!/3
E. 8!/6

This question is created by me, I couldn't find similar question in the forum:


I will never forget the lesson on combinatorics presented by mikemcgarry on Magoosh.
so..we have 8 different letters. these can be arranged in 8! ways.
for every possible way when A comes after Q, there is a combination when A comes before Q. so we need to divide by 2.

8!/2 = 8*7!/2 => 4*7!
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 20873
Re: How many words can be formed using all the letters of "EQUAT [#permalink] New post  23 Oct 2020, 05:54
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: How many words can be formed using all the letters of "EQUAT [#permalink]
23 Oct 2020, 05:54
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
10608 posts
Bunuel
Math Expert
82990 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2791 posts
generis
Senior SC Moderator
5132 posts

cron

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