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

It is currently 09 Dec 2019, 19:06

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

All the possible five-digit numbers are formed using only the digits

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
S
Joined: 18 Jul 2019
Posts: 54
Premium Member Reviews Badge CAT Tests
All the possible five-digit numbers are formed using only the digits  [#permalink]

Show Tags

New post 25 Nov 2019, 01:20
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

46% (02:11) correct 54% (02:12) wrong based on 13 sessions

HideShow timer Statistics

All the possible five-digit numbers are formed using only the digits 4, 5 and 6. How many of them will have at least two fives?

(A) 131
(C) 195
(B) 219
(D) 230
(E) 250
Director
Director
User avatar
V
Joined: 27 May 2012
Posts: 945
All the possible five-digit numbers are formed using only the digits  [#permalink]

Show Tags

New post 25 Nov 2019, 08:17
CaptainLevi wrote:
All the possible five-digit numbers are formed using only the digits 4, 5 and 6. How many of them will have at least two fives?

(A) 131
(C) 195
(B) 219
(D) 230
(E) 250


Total cases \((3)^4\) - ( Ways to get no five + ways to get one five ) = Ways to get at least two five.

No five's =2*2*2*2*2 = 32

Number of ways to get ONLY one 5:
One five and rest all 4 ( 5, 4, 4, 4, 4) = \(\frac{5!}{4!}= 5\) ways
One five and rest all 6 ( 5, 6, 6, 6, 6) = \(\frac{5!}{4!}= 5\) ways
One five ,three 6 and one 4 ( 5, 6, 6, 6, 4) =\(\frac{5!}{3!}=20\) ways
One five ,three 4 and one 6( 5, 4, 4, 4, 6)=\(\frac{5!}{3!}\)=20 ways
One five ,two 6 and two 4 ( 5 6 6 4 4) =\(\frac{5!}{2!*2!}\)=30 ways

So total ways=\((3)^4\)=243
No fives in = 32 ways
One five in = 5+5+20+20+30 =80 ways
So 243 - (32+80)= 131 Ways to get at least two five's.

Ans- A
_________________
- Stne
Intern
Intern
avatar
B
Joined: 19 Jan 2019
Posts: 11
Re: All the possible five-digit numbers are formed using only the digits  [#permalink]

Show Tags

New post 26 Nov 2019, 03:02
any other way to solve this ?
Intern
Intern
avatar
B
Joined: 19 Jan 2019
Posts: 11
Re: All the possible five-digit numbers are formed using only the digits  [#permalink]

Show Tags

New post 26 Nov 2019, 03:05
how is it 3 raise to the power 4 ?
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: All the possible five-digit numbers are formed using only the digits  [#permalink]

Show Tags

New post 26 Nov 2019, 05:11
1
CaptainLevi wrote:
All the possible five-digit numbers are formed using only the digits 4, 5 and 6. How many of them will have at least two fives?

(A) 131
(C) 195
(B) 219
(D) 230
(E) 250



Five digit number: ____ ____ ____ ____ ____

Each blank can be filled up in 3 ways. So there are 3 * 3 * 3 * 3 * 3 = 243 ways of making the five digit number.

In how many of them will there be no 5? There will be no 5 in numbers made from only 4 and 6. So each spot will have only 2 options in that case.
Then there are 2 * 2 * 2 * 2 * 2 = 32 ways of making the five digit number.

In how many of them will there be only one 5? Select 1 spot for the 5 out of 5 spots in 5 ways.
The number of ways of filling up each of the other 4 spots is 2.
Total numbers = 5 * 2 * 2 * 2 * 2 = 80 ways of making the five digit number.

So in 32 + 80 = 112 numbers, there will be no 5 or only one 5.

In the other 243 - 112 = 131 numbers, there will be at least two 5s.

Answer (A)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: All the possible five-digit numbers are formed using only the digits   [#permalink] 26 Nov 2019, 05:11
Display posts from previous: Sort by

All the possible five-digit numbers are formed using only the digits

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





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