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

It is currently 17 Oct 2019, 08:31

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.

Close

Request Expert Reply

Confirm Cancel

Five letters A, P, P, L and E are listed in a row. How many arrangemen

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42
GPA: 3.82
Five letters A, P, P, L and E are listed in a row. How many arrangemen  [#permalink]

Show Tags

New post 01 Oct 2018, 00:40
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (01:30) correct 47% (01:30) wrong based on 70 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

Five letters A, P, P, L and E are listed in a row. How many arrangements have at least one letter between the two Ps?

A. 24
B. 30
C. 36
D. 42
E. 48

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: Five letters A, P, P, L and E are listed in a row. How many arrangemen  [#permalink]

Show Tags

New post 01 Oct 2018, 02:50
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Five letters A, P, P, L and E are listed in a row. How many arrangements have at least one letter between the two Ps?

A. 24
B. 30
C. 36
D. 42
E. 48


Total Arrangements of all letters = 5!/2! = 60
Total Arrangements of all letters with two Ps together = 4! = 24

Total arrangements with two Ps together (i.e. atleast one letter between two Ps) = 60-24 = 36

Answer: Option C
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Senior Manager
Senior Manager
avatar
G
Joined: 04 Aug 2010
Posts: 475
Schools: Dartmouth College
Re: Five letters A, P, P, L and E are listed in a row. How many arrangemen  [#permalink]

Show Tags

New post 01 Oct 2018, 06:05
1
2
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Five letters A, P, P, L and E are listed in a row. How many arrangements have at least one letter between the two Ps?

A. 24
B. 30
C. 36
D. 42
E. 48


Good arrangements = total arrangements - bad arrangements.

Total arrangements:
Number of ways to arrange 5 elements = 5!.
But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED.
The reason:
When the identical elements swap positions, the arrangement doesn't change.
Here, we must divide by 2! to account for the two identical P's:
5!/2! = 60.

Bad arrangements:
In a bad arrangement, the two P's are in adjacent slots.
Let [PP] represent the 2 adjacent P's.
Number of ways to arrange the 4 elements [PP], D, G and T = 4! = 24.

Good arrangements:
Total arrangements - bad arrangements = 60-24 = 36.


_________________
GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Five letters A, P, P, L and E are listed in a row. How many arrangemen  [#permalink]

Show Tags

New post 01 Oct 2018, 09:52
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Five letters A, P, P, L and E are listed in a row. How many arrangements have at least one letter between the two Ps?

A. 24
B. 30
C. 36
D. 42
E. 48


Here's an approach that doesn't require us to subtract the bad arrangements.

Take the task of arranging the 5 letters and break it into stages.

Stage 1: Arrange the letters A, L, E in a row
We can arrange n unique objects in n! ways.
So, we can arrange the 3 letters in 3! ways (= 6 ways)
So, we can complete stage 1 in 6 ways

IMPORTANT: For each arrangement of 3 letters (above), there are 4 places where the two P's can be placed.
For example, in the arrangement AEL, we can add spaces as follows _A_E_L_
So, if we place each P in one of the available spaces, we can ENSURE that the two P's are never together.

Stage 2: Select two available spaces and place an P in each space.
Since the order in which we select the two spaces does not matter, we can use combinations.
We can select 2 spaces from 4 spaces in 4C2 ways (= 6 ways)
So we can complete stage 2 in 6 ways.

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus arrange all 5 letters) in (6)(6) ways (= 36 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So be sure to learn this technique.

RELATED VIDEOS



_________________
Test confidently with gmatprepnow.com
Image
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Five letters A, P, P, L and E are listed in a row. How many arrangemen  [#permalink]

Show Tags

New post 03 Oct 2018, 02:26
=>

When we encounter “at least” in counting questions or probability questions, we should consider complementary counting.
The total number of arrangements of the 5 letters is 5!/2! (5! Counts each arrangement of the two Ps 2! times).
The number of arrangements with no letter between the two Ps is 4!.
Thus, the number of arrangements in which at least one letter lies between the two Ps is 5!/2! – 4! = 60 – 24 = 36.

Therefore, C is the answer.
Answer: C
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: Five letters A, P, P, L and E are listed in a row. How many arrangemen   [#permalink] 03 Oct 2018, 02:26
Display posts from previous: Sort by

Five letters A, P, P, L and E are listed in a row. How many arrangemen

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne