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

It is currently 18 Apr 2019, 09:49

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

In how many ways can 3-digit numbers be formed selecting 3 d

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

Hide Tags

 
Manager
Manager
User avatar
Joined: 24 Sep 2008
Posts: 167
Schools: MIT / INSEAD / IIM - ABC
In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post Updated on: 27 Jul 2015, 09:16
17
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

42% (01:58) correct 58% (01:26) wrong based on 194 sessions

HideShow timer Statistics

In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!

Originally posted by GODSPEED on 16 Aug 2009, 04:13.
Last edited by Bunuel on 27 Jul 2015, 09:16, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Intern
Intern
avatar
Joined: 10 Jul 2009
Posts: 39
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 19 Aug 2009, 21:39
1
GODSPEED wrote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

1. 5P3/(2!)
2. 4P3
3. 4^3
4. 4P3+3C1*(3!/2!)
5. 60 × 3!


My answer is 4P3. We should discard a double digit. We only have 4 distinctive numbers to choose from.
Manager
Manager
User avatar
Joined: 14 Aug 2009
Posts: 117
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 19 Aug 2009, 23:45
1
1
tomirisk wrote:
GODSPEED wrote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

1. 5P3/(2!)
2. 4P3
3. 4^3
4. 4P3+3C1*(3!/2!)
5. 60 × 3!


My answer is 4P3. We should discard a double digit. We only have 4 distinctive numbers to choose from.


can't discard duplicated digits, for instance, the number can be 121.

the right one should be 5P3-3(3P2+3P1)=33

answer is C.
_________________
Kudos me if my reply helps!
Intern
Intern
avatar
Joined: 10 Jul 2009
Posts: 39
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 20 Aug 2009, 04:40
flyingbunny wrote:
tomirisk wrote:
GODSPEED wrote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

1. 5P3/(2!)
2. 4P3
3. 4^3
4. 4P3+3C1*(3!/2!)
5. 60 × 3!


My answer is 4P3. We should discard a double digit. We only have 4 distinctive numbers to choose from.


can't discard duplicated digits, for instance, the number can be 121.

the right one should be 5P3-3(3P2+3P1)=33

answer is C.


you are right flyingbunny that we can't discard a double digit. But answer C=4^3=64
and your solution 5P3-3(3P2+3P1)= 34. how can it be C?
Manager
Manager
User avatar
Joined: 14 Aug 2009
Posts: 117
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 20 Aug 2009, 05:16
ha, 5P3-3(3P2+3P1)=60-3*9=33
answer is 4. 4P3+3C1*(3!/2!)=33.
_________________
Kudos me if my reply helps!
Senior Manager
Senior Manager
User avatar
Joined: 11 Dec 2008
Posts: 443
Location: United States
GMAT 1: 760 Q49 V44
GPA: 3.9
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 20 Aug 2009, 13:25
1
Umm... you want to explain your solution for laypeople? 8-)
Manager
Manager
User avatar
Joined: 25 Aug 2009
Posts: 127
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 05 Jan 2010, 19:42
2
1
For those of you who need a detailed explanation
Lets find the number of 3 digit numbers with only single 1.
i.e. 3 digit numbers from 1,2,3,4
i.e. 4P3 (since order is important)

Next we find numbers with two 1s in it.
the third digit can be chosen in 3C1 ways and the numbers can be arranged in !3 ways, but 2 numbers are the same hence we divide by !2 (Formula used - number of ways of arranging p things which have q things of one kind, r things of another kind and so on is !p/(!q+!r+...))
Finally we have 3C1*(!3/!2))

Add the above two to get the answer D.
Hope this helps
_________________
Rock On
Manager
Manager
avatar
Joined: 27 Aug 2009
Posts: 78
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 06 Jan 2010, 12:28
Thanks for the explanation
Intern
Intern
avatar
Joined: 20 Dec 2009
Posts: 11
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 08 Jan 2010, 05:23
I've a doubt regarding the answer and explanation given.
The question does not mention any constrain on the repetition of digits, so we can have 4 distinct choices for each position of the 3-digited number and hence we have
4^3 = 64 such numbers.
Can any one explain why this can't be the answer?

TIA.
Manager
Manager
User avatar
Joined: 05 Jul 2008
Posts: 129
GMAT 2: 740 Q51 V38
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 09 Jan 2010, 07:13
ashueureka wrote:
I've a doubt regarding the answer and explanation given.
The question does not mention any constrain on the repetition of digits, so we can have 4 distinct choices for each position of the 3-digited number and hence we have
4^3 = 64 such numbers.
Can any one explain why this can't be the answer?

TIA.

Quote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

It means you just have 1 digit 2, 1 digit 3, 1 digit 4 and 2 digits 1 to form a number.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7556
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 09 Jan 2010, 09:46
hi expl of correct ans..
there are four different digits so no of ways 3 digits can be chosen... 4P3...
rest 3 digit nos will have two 1's and a digit from rest 3.... 3!/2!(noof ways when two digits are same)*3C1(3 different digits)... so ans is 4P3+3!/2!*3C1...D
_________________
Intern
Intern
avatar
Joined: 16 Nov 2015
Posts: 17
In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post Updated on: 18 Feb 2016, 03:37
GODSPEED wrote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!



This problem is written poorly. Anyways it has to state that 1,1,2,3,4 is a set of numbers. So you you can use each element (number) for once. From this perspective solution is easy: There are two cases. Numbers with single 1 and numbers with double 1. Which is 4P3 + 3C1 * 3C2 (Answer D)

Originally posted by leve on 25 Jan 2016, 07:24.
Last edited by leve on 18 Feb 2016, 03:37, edited 1 time in total.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2556
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 17 Feb 2016, 20:05
excuse me, but WTF is P? where did u see such notations in official gmat questions??
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7556
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 17 Feb 2016, 20:32
1
mvictor wrote:
excuse me, but WTF is P? where did u see such notations in official gmat questions??


Hi,
P means permutation and is COUSION, or I should say REAL BROTHER of C, combinations..
only thing is P is very concerned about the order/ sequence, so generally turns out to be not only real brother BUT a BIG BRO too of C ..

so when 5C2 means 5!/3!2!..
5P2 means 5!/3!2! * 2! = 5!/3!, as these two selected can be arranged in 2! ways..
so when you select it is C, and when you arrange, it is P..


Hope it clears some air around the the F of WTF, P :) :)
_________________
Manager
Manager
avatar
Joined: 24 May 2013
Posts: 79
GMAT ToolKit User
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 19 Mar 2016, 10:15
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!

Had it asked for all the different nos instead of 1,1,2,3,4 the ans wuld be: 5P3/2! = 30
In this solution we hav also halved (divided by 2!) the numbers containing 2,3 and 4.
The numbers containing 2,3,4 are 6.
Add 6/2 =3 back to 30 and we get the answer i.e. 30+3=33.
Hence D is the answer.

thanks
Manager
Manager
avatar
Joined: 01 Mar 2014
Posts: 111
Schools: Tepper '18
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 19 Mar 2016, 21:22
chetan2u wrote:
hi expl of correct ans..
there are four different digits so no of ways 3 digits can be chosen... 4P3...
rest 3 digit nos will have two 1's and a digit from rest 3.... 3!/2!(noof ways when two digits are same)*3C1(3 different digits)... so ans is 4P3+3!/2!*3C1...D


I am having trouble understanding this concept. Can you please explain why we cannot consider these as 5 different digits? How does the repetition of a number have an impact? Really grateful for an explanation.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7556
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 19 Mar 2016, 21:32
MeghaP wrote:
chetan2u wrote:
hi expl of correct ans..
there are four different digits so no of ways 3 digits can be chosen... 4P3...
rest 3 digit nos will have two 1's and a digit from rest 3.... 3!/2!(noof ways when two digits are same)*3C1(3 different digits)... so ans is 4P3+3!/2!*3C1...D


I am having trouble understanding this concept. Can you please explain why we cannot consider these as 5 different digits? How does the repetition of a number have an impact? Really grateful for an explanation.


Hi,

Quote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!


say we take these as five different digits..
let these be-
1=a, 1=b, 2=c, 3=d, 4=e..

now we have to choose three digits/letters
so these numbers could be:-
abc=112
bac=112
acd=123
bcd=123 and so on


see here you are taking acd and bcd ; and abc - bac as two different 3-digit numbers, but they are the same..
so to avoid REPETITIONS we take them as 4 different digits


so we consider 5- digits given as 4 different digits to find numbers with all different digits..
example 123,124,234 etc

and then we consider similar digits as two digits and make combinations with remaining digits
example
112, 121, 131,113 and so on

Hope it helps

_________________
Manager
Manager
avatar
Joined: 01 Mar 2014
Posts: 111
Schools: Tepper '18
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 19 Mar 2016, 22:03
chetan2u wrote:
MeghaP wrote:
chetan2u wrote:
hi expl of correct ans..
there are four different digits so no of ways 3 digits can be chosen... 4P3...
rest 3 digit nos will have two 1's and a digit from rest 3.... 3!/2!(noof ways when two digits are same)*3C1(3 different digits)... so ans is 4P3+3!/2!*3C1...D


I am having trouble understanding this concept. Can you please explain why we cannot consider these as 5 different digits? How does the repetition of a number have an impact? Really grateful for an explanation.


Hi,

Quote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!


say we take these as five different digits..
let these be-
1=a, 1=b, 2=c, 3=d, 4=e..

now we have to choose three digits/letters
so these numbers could be:-
abc=112
bac=112
acd=123
bcd=123 and so on


see here you are taking acd and bcd ; and abc - bac as two different 3-digit numbers, but they are the same..
so to avoid REPETITIONS we take them as 4 different digits


so we consider 5- digits given as 4 different digits to find numbers with all different digits..
example 123,124,234 etc

and then we consider similar digits as two digits and make combinations with remaining digits
example
112, 121, 131,113 and so on

Hope it helps


It makes sense now. Extremely daft of me to not see that. Thank you so much, much appreciated..!! :)
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 718
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 13 Aug 2017, 22:16
1
GODSPEED wrote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!


Given digits : 1,1,2,3,4
There can be 2 cases for forming 3 digit numbers.

Case 1 : When 1 is used only once and we need to form the 3-digit number from digits 1,2,3,4 (Nos. like 123,234, etc.)
No. of such numbers = 4P3

Case 2 : When 1 is used twice and 3rd digit is taken from 2,3,4 (Nos. like 113,141, etc.)
No. of such numbers = 3C1*3!/2! (3C1 for selecting one number out of 3 numbers 2,3,4; 3! means arranging the 3 numbers 1,1 and 3rd selected number and it is divided by 2! as there are 2 1's. Due to which many numbers will be similar.)

Total numbers : 4P3 + 3C1*3!/2!

Answer D
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2825
Re: In how many ways can 3-digit numbers be formed selecting 3 d  [#permalink]

Show Tags

New post 18 Aug 2017, 09:06
GODSPEED wrote:
In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)
B. 4P3
C. 4^3
D. 4P3+3C1*(3!/2!)
E. 60 × 3!



We will separate the 3-digit numbers into two types: Those that contain two 1s and those that contain at most one 1.

1) The numbers that contain two 1s:

These numbers will be of the form _11, 1_1, or 11_, where _ is a digit of 2, 3, or 4. So, there are a total of 9 such numbers.

2) The numbers that contain at most one 1:

These numbers will consist of 3 of the digits 1, 2, 3, and 4. Since the order is important, there are 4P3 such numbers.

Scanning the answer choices, we see that D is the correct answer.

Answer: D
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

GMAT Club Bot
Re: In how many ways can 3-digit numbers be formed selecting 3 d   [#permalink] 18 Aug 2017, 09:06

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

In how many ways can 3-digit numbers be formed selecting 3 d

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.