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.
Hello Guest!
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join 700,000+ 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 Prep. 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!
and many more benefits!
- Register now! It`s easy!
- Already registered? Sign in!
Sep 24
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a masterclass to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days.
Sep 25
Attend this webinar to learn a methodical approach to recall rules with ease and score consistently high on GMAT SC questions.
Sep 25
Attend this webinar to learn the core NP concepts and a structured approach to solve 700+ Number Properties questions in less than 2 minutes.
Senior Manager
Joined: 31 Oct 2010
Status:Up again.
Posts: 428
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
00:00
Question Stats:
Hide Show timer Statistics
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A. 210
B. 1050
C. 25200
D. 21400
E. 42800
Guys I've some concerns on this problem and I've put them under the spoiler. Please help me out!Thanks..
_________________
My GMAT debrief: //gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 6807
Location: Canada
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
gmatpapa wrote:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.
210
B. 1050
C. 25200
D. 21400
E. 42800
Take the task of creating 5-letter words and break it into stages.
Stage 1: Select the 3 consonants to work with
Since the order in which we select the consonants does not matter, we can use combinations.
We can select 3 consonants from 7 consonants in 7C3 ways (= 35 ways)
Stage 2: Select the 2 vowels to work with
Since the order in which we
select the vowels does not matter, we can use combinations.
We can select 2 vowels from 4 vowels in 4C2 ways (= 6 ways)
If anyone is interested, we have a video on calculating combinations (like 4C2) in your head - see below
Stage 3: Take the 5 selected letters and arrange them.
We can complete this stage in 5! ways (= 120 ways).
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25,200 ways)
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
RELATED VIDEOS
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant
score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Manager
Joined: 09 Aug 2010
Posts: 60
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
Using 4 x 3 / (2 x 1) = 6, to select your vowels... just calculated the number of groupings.
Example:
a e i o (4
vowels)
6 POSSIBLE GROUPINGS
a e
a i
a o
e i
e o
i o
If you take the ARRANGEMENT into account,
you should have 12 instead of 6.
a e
a i
a o
e i
e o
i o
e a
i a
o a
i e
o e
o i
But it's best to just get the possible number of grouping first which is 7C3 4C2 = 210. Then we arrange it by multiplying to 5!.. So as to allow consonants and vowels alternating...
Ex.
c d f e i
This will allow c d e i f.. Alternating elements...
Retired Moderator
Joined: 16 Nov 2010
Posts: 1011
Location: United States (IN)
Concentration: Strategy, Technology
Re: Out of 7
consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
7C3 * 4C2 * 5!
(7 * 6 * 5)/3! * 4!/2!2! * 120
35 * 6 * 120
= 210 * 120
= 25200
I don't
understand what is need of arranging the 5 letters again, as 7C3*4C2 will do that already.
7C3*4C2 will select letters, thereafter one has to arrange those.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership - big benefits and savings
Senior Manager
Joined: 31 Oct 2010
Status:Up again.
Posts: 428
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
subhashghosh wrote:
7C3 * 4C2 * 5!
(7 * 6 * 5)/3! * 4!/2!2! * 120
35 * 6 * 120
= 210 * 120
= 25200
I don't understand what is need of arranging the 5 letters again, as 7C3*4C2 will do that already.
7C3*4C2 will select letters, thereafter one has to arrange those.
Uh.. thanks I think I got it now..
Say for example, the first combination is "r t y u i" You can sure arrange it in 5! ways, and since this is a unique combination, alphabets can be arranged in 5! and still form words not contained in any of the other combinations.
Thanks for pointing out. great tip!
_________________
My GMAT debrief: //gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html
Senior Manager
Joined: 01 Feb 2011
Posts: 393
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
7c3*4c2*5!
= 25200
Answer is C.
Director
Joined: 08 May 2009
Status:There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Posts: 607
Re: Out of 7 consonants and 4 vowels, how many words of
3 consonants and 2 [#permalink]
5 letters in the word - hence 5! ways of arranging them.
positions - - - - -
7* 6 *5 * 4 * 3
consonants vowels
Thus without actually multiplying one can deduce like this : 5! = 120 means the number is divisible by 3.D and E POE.
Also, the number must have 2 zeros at the units and tens place, 120 and 6*5 = 30 is there.
C is a perfect fit.
Current Student
Joined: 16 Jan 2019
Posts: 649
Location: India
Concentration: General Management
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
I think the question needs to mention that repetition of letters is not allowed
Posted from my mobile device
_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 6807
Location: Canada
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
firas92 wrote:
I think the question needs to mention that repetition of letters is not allowed
Posted from my mobile device
Agreed! Otherwise, words like AABBB would be allowed.
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and
the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2549
Concentration: Operations, Strategy
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
GMATPrepNow wrote:
firas92 wrote:
I think the question needs to mention that repetition of letters is not allowed
Posted from my mobile device
Agreed! Otherwise, words like AABBB would be allowed.
أHi GMATPrepNow Brent
How will be the solution if repetition would allowed? what will change in way to solve it?
Thanks in advance
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 6807
Location: Canada
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
Mo2men wrote:
GMATPrepNow wrote:
firas92 wrote:
I think the question needs to mention that repetition of letters is not allowed
Posted from my mobile device
Agreed! Otherwise, words like AABBB would be allowed.
أHi GMATPrepNow Brent
How will be the solution if repetition would allowed? what will change in way to solve it?
Thanks in advance
That rewording would require us to consider many different cases:
5-letter words with 2 different vowels and 3 different consonants
5-letter words with 2 identical vowels and 3 different consonants
5-letter words with 2
different vowels, 2 identical consonants, and 1 different consonant
5-letter words with 2 identical vowels, 2 identical consonants, and 1 different consonant
5-letter words with 2 different vowels, and 3 identical consonants
5-letter words with 2 identical vowels, and 3 identical consonants
Phew! I'm already tired.
As you might imagine, the reworded question would take up wayyyyyyy too much time to be a true GMAT question.
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more
VP
Joined: 04 Aug 2010
Posts: 1232
Schools:Dartmouth College
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
Given the OA, the prompt should read as follows:
gmatpapa wrote:
Out of 7 DISTINCT consonants and 4 DISTINCT vowels, how many words of 3 consonants and 2 vowels can be formed, if no letter may appear in the word more than once?
A. 210
B. 1050
C. 25200
D. 21400
E. 42800
One approach:
From the 5 positions in the word, the number of ways to choose 3 positions for
the 3 consonants = 5C3 = \(\frac{5*4*3}{3*2*1} = 10\)
From the remaining 2 positions in the word, the number of ways to choose 2 positions for the 2 vowels = 2C2 \(= \frac{2*1}{2*1} = 1\)
Number of options for the first consonant = 7 (Any of the 7 consonants)
Number of options for the second consonant = 6 (Any of the 6 remaining consonants)
Number of options for the third consonant = 5 (Any of the 5 remaining consonants)
Number of options for the first vowel = 4 (Any of the 4
vowels)
Number of options for the second vowel = 3 (Any of the 3 remaining vowels)
To combine the options above, we multiply:
10*1*7*6*5*4*3 = 25200
_________________
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been
admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As your tutor, I won't simply teach you how I would approach problems.
I'll unlock the best way for YOU to solve problems.
Available all over the world for virtual sessions and in NYC for live sessions.
For more information, please email me at .
Non-Human User
Joined: 09 Sep 2013
Posts: 24390
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
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: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]
20 Dec 2021, 05:47
Moderators:
Senior Moderator - Masters Forum
3086 posts