GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Mar 2019, 23:42

### 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

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

# In how many ways all the letters of the word WEAPONS can be arranged

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2722
In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

05 Mar 2019, 21:42
00:00

Difficulty:

65% (hard)

Question Stats:

21% (02:41) correct 79% (01:29) wrong based on 19 sessions

### HideShow timer Statistics

In how many ways all the letters of the word WEAPONS can be arranged such that in any of the arrangements, no two vowels will be together?

A. $$^5C_3 * 3!$$

B. $$3! * 4!$$

C. $$^5C_3 * 4!$$

D. $$7! – 5! * 3!$$

E. $$^5C_3 * 3! * 4!$$

_________________

Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

SVP
Joined: 18 Aug 2017
Posts: 2497
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

Updated on: 08 Mar 2019, 03:16
WEAPONS = 7! ways total arrangement
vowels = EAO 3! ways and consonants WPNS = 4! ways

these vowels can be arranged in 5c3 ways between 4 WPNS

5c3*3!*4!
IMO E

EgmatQuantExpert wrote:
In how many ways all the letters of the word WEAPONS can be arranged such that in any of the arrangements, no two vowels will be together?

A. $$^5C_3 * 3!$$

B. $$3! * 4!$$

C. $$^5C_3 * 4!$$

D. $$7! – 5! * 3!$$

E. $$^5C_3 * 3! * 4!$$

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 06 Mar 2019, 01:57.
Last edited by Archit3110 on 08 Mar 2019, 03:16, edited 1 time in total.
Intern
Joined: 23 Oct 2013
Posts: 28
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

06 Mar 2019, 19:23
is ans E

arrange consonants as _W_P_N_S_ consonants E,A,O can be placed in any 5 blanks so 5c3

consonants can be arranged within itself in 3!
vowels can be arranged in 4! ways

so 5c3*4!*3!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2722
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

07 Mar 2019, 22:42

Solution

Given:
In this question, we are given
• A specific word is given: WEAPONS, of which all the letters can be arranged to form different words

To find:
We need to determine
• How many such arrangements are possible, where no two vowels will be together

Approach and Working:
In the given word “WEAPONS”, there are 4 consonants: W, P, N, S and 3 vowels: E, A, O.
• When we say that no two vowels are together, it means there will be at least one consonant between any two vowels.

As there are 4 consonants, let us first put them, as shown in the following figure:

Now, for the 3 vowels, there will be actually 5 places where any of those vowels can be placed.

• Out of the 5 possible places, 3 will be chosen for the vowels in $$^5C_3$$ ways.
• Also, the vowels can rearrange themselves in 3! ways and the consonants can rearrange themselves in 4! ways.
• Therefore, the total number of possible arrangements = $$^5C_3 * 3! * 4!$$

Hence, the correct answer is option E.

_________________

Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2722
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

07 Mar 2019, 22:45
Archit3110 wrote:
WEAPONS = 7! ways total arrangement
vowels = EAO WPNS = 5! ways and total vowels = 3 ;3! ways

7!-5!*3!
IMO D

Hey Archit3110,
In your calculation, you missed those cases where two vowels can be together. You only removed the cases where all 3 vowels are together.
_________________

Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 119
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

07 Mar 2019, 23:57
1
There are 7 letters in the word WEAPONS with 3 vowels and 4 consonant of the 5 possible places, 3 will be chosen for the vowels in 5C35C3 ways.the vowels can rearrange themselves in 3! ways and the consonants can rearrange themselves in 4! ways.. Hence, number of arrangements of letters such that all vowels are all together is 5C3∗3!∗4! so the correct answer is E
_________________
Give a kudos if u find my post helpful. kudos motivates active discussions

Intern
Joined: 13 Jul 2018
Posts: 5
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

08 Mar 2019, 01:55
1
EgmatQuantExpert wrote:
Archit3110 wrote:
WEAPONS = 7! ways total arrangement
vowels = EAO WPNS = 5! ways and total vowels = 3 ;3! ways

7!-5!*3!
IMO D

Hey,
In your calculation, you missed those cases where two vowels can be together. You only removed the cases where all 3 vowels are together.

And what is the best way to do it with that approach? (removing csaes from the total)
SVP
Joined: 18 Aug 2017
Posts: 2497
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

08 Mar 2019, 03:13
EgmatQuantExpert wrote:
Archit3110 wrote:
WEAPONS = 7! ways total arrangement
vowels = EAO WPNS = 5! ways and total vowels = 3 ;3! ways

7!-5!*3!
IMO D

Hey Archit3110,
In your calculation, you missed those cases where two vowels can be together. You only removed the cases where all 3 vowels are together.

EgmatQuantExpert
yeah i made an error.. misread question.. edited thanks..
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 21 Sep 2016
Posts: 5
Location: Saudi Arabia
Concentration: Finance, Entrepreneurship
WE: Corporate Finance (Consumer Electronics)
In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

09 Mar 2019, 08:30
When we insert 1 vowel in the middle of each consonant and 1 vowel each at the corner, in total, it would make 9 spaces, however WEAPONS has only 7 spaces.
In how many ways all the letters of the word WEAPONS can be arranged   [#permalink] 09 Mar 2019, 08:30
Display posts from previous: Sort by

# In how many ways all the letters of the word WEAPONS can be arranged

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.