MBA Spotlight – The Biggest MBA Fair is June 13-14
closeclose
It is currently 09 Jun 2023, 15:15
Register
GMAT Club Tests
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

We are required to form different words with the help of letters of th

6 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88754
CAT Tests Forum Quiz Mode Top Member of the Month
We are required to form different words with the help of letters of th [#permalink] New post  01 Nov 2019, 05:47
27
Bookmarks
Expert Reply
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:

95% (hard)

Question Stats:

53% (02:35) correct 47% (02:45) wrong based on 369 sessions

Hide Show timer Statistics

We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
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
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
avatar
L
Dillesh4096
VP
VP
Joined: 20 Jul 2017
Posts: 1310
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Re: We are required to form different words with the help of letters of th [#permalink] New post  01 Nov 2019, 06:21
2
Bookmarks
Bunuel wrote:
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


Are You Up For the Challenge: 700 Level Questions


Formula: Not together = Total ways - no of ways when together

Number of ways when I&N together = arranging the letters {IN, T, E, G, E, R} in a straight line = 6!*2!/2! = 6! = 720

Total ways of arranging INTEGER = 7!/2! = 2520

Not together, m1 = 2520 - 720 = 1800

Number of ways which begin with I and end with R is same as arranging the letters {N, T, E, G, E} in the given spaces I, _, _, _, _, _, R = 5!/2! = 60 = m2

m1/m2 = 1800/60 = 30

IMO Option C

Posted from my mobile device
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7520
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: We are required to form different words with the help of letters of th [#permalink] New post  01 Nov 2019, 07:55
Bunuel wrote:
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


Are You Up For the Challenge: 700 Level Questions


INTEGER can be arranged in 7!/2! ways = 2520
M1 = m1 be the number of words in which I and N are never together = INTEGER ; XTEGER = 6!/2!*2c1 ; 720
so M1 = 2520-720 ; 1800
M2 = m2 be the number of words which begin with I and end with R ; I NTEGE R ; 5!/2! ; 60 ways
ratio M1/M2 = 1800/60 ; 30
IMO C
avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1747
Location: United States
Re: We are required to form different words with the help of letters of th [#permalink] New post  25 Mar 2020, 08:04
1
Bookmarks
Bunuel wrote:
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


INT-EGE-R has 7 letters, 2 identical (E), so 6 distinct
p(INTEGER)=7!/2!
P([IN]TEGER)=6!/2!*2C1 (because we can begin with [IN] or [NI])
P(without [IN])=7!/2!-6!=(7!-2*6!)/2!=(6!(7-2))/2!)=6!(5)/2!
P([I]NTEGE[R])=5!/2!
m1/m2=6!(5)/2!/5!/2!=6!(5)/2!*2!/5!=6*5=30

Ans (C)
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5008
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge
We are required to form different words with the help of letters of th [#permalink] New post  28 Mar 2020, 03:13
Bunuel wrote:
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


Are You Up For the Challenge: 700 Level Questions


Given:
1. We are required to form different words with the help of letters of the word INTEGER.
2. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R.

Asked: what is the value of m1/m2?

INTEGER consists of: -
I-1
N-1
T-1
E-2
G-1
R-1

Total words formed = 7!/2! = 2520
Words in which I and N are together = 2* 6!/2! = 720
m1 = 2520 - 720 = 1800

m2 = Number of Words which begin with I and end with R. = 5!/2! = 60

m1/m2 = 1800/60 = 30

IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 27952
Re: We are required to form different words with the help of letters of th [#permalink] New post  04 Feb 2023, 00:23
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: We are required to form different words with the help of letters of th [#permalink]
04 Feb 2023, 00:23
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
88754 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3142 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