It is currently 21 Apr 2018, 14:05

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit

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

Hide Tags

Manager
Manager
User avatar
S
Joined: 17 Oct 2016
Posts: 87
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Premium Member Reviews Badge
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 18 Sep 2017, 19:58
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

61% (00:31) correct 39% (00:26) wrong based on 107 sessions

HideShow timer Statistics

In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition

A. 12

B. 24

C. 18

D. 4

E. 28
[Reveal] Spoiler: OA

_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik



Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5774
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 18 Sep 2017, 20:39
fitzpratik wrote:
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition

A. 12

B. 24

C. 18

D. 4

E. 28



So Number is ABCD.
Be careful how many can replace A as there is ZERO and you should get the correct answer..
A can be replaced by 2,4,7....3 ways
B can be replaced by remaining 3 as one is used in place of A....3 ways
C, by remaining 2
D by the left over

So arrangements = 3*3*2*1=18

C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

2 KUDOS received
Manager
Manager
User avatar
G
Joined: 22 May 2015
Posts: 102
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 18 Sep 2017, 22:11
2
This post received
KUDOS
1
This post was
BOOKMARKED
No of 4 digit numbers possible - 4!
No of 3 digit numbers possible - 3!
So correct 4 digit numbers is 4! - 3! = 24 - 6 = 18
_________________

Consistency is the Key

Manager
Manager
User avatar
S
Joined: 17 Oct 2016
Posts: 87
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Premium Member Reviews Badge
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 18 Sep 2017, 22:21
0 as a digit in this question makes the question interesting.

Answer changes as soon as the "0" is replaced by 2 or any other digit.
_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik



Intern
Intern
avatar
Joined: 25 Aug 2017
Posts: 2
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 20 Sep 2017, 04:56
fitzpratik wrote:
0 as a digit in this question makes the question interesting.

Answer changes as soon as the "0" is replaced by 2 or any other digit.

Why cant the numbers starting from 0 be considered in this scenario?

I mean 0472 may be a distinct number on a code.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44599
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 20 Sep 2017, 05:11
johneagle2776 wrote:
fitzpratik wrote:
0 as a digit in this question makes the question interesting.

Answer changes as soon as the "0" is replaced by 2 or any other digit.

Why cant the numbers starting from 0 be considered in this scenario?

I mean 0472 may be a distinct number on a code.


We are NOT looking for 4-digit codes, we are looking for 4-digit numbers, so while a 4-digit code can start with 0 (for example 0123 code is a valid 4-digit code), a 4-digit number cannot start with 0 (0123 is NOT a 4-digit number, it's a 3-digit number 123).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
S
Joined: 17 Oct 2016
Posts: 87
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Premium Member Reviews Badge
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 20 Sep 2017, 05:15
@johneagle
Bunuel is correct, each and every word of a question stem matters. If the word "number" was to be replaced by "codes" or "arrangement of 4 digits", answer would change.
_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik



Intern
Intern
avatar
B
Joined: 23 Oct 2013
Posts: 4
WE: Consulting (Law)
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 20 Sep 2017, 08:29
The answer is C: 18
3x3x2x1 = 18
Intern
Intern
avatar
B
Joined: 31 Jul 2017
Posts: 7
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 22 Sep 2017, 17:10
laddaboy wrote:
No of 4 digit numbers possible - 4!
No of 3 digit numbers possible - 3!
So correct 4 digit numbers is 4! - 3! = 24 - 6 = 18


Could you explain the thought process behind this. Why aren't you subtracting the number of 2 digits possible and number of 1 digits possible.
1 KUDOS received
Manager
Manager
User avatar
G
Joined: 22 May 2015
Posts: 102
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 24 Sep 2017, 18:06
1
This post received
KUDOS
akhan126 wrote:
laddaboy wrote:
No of 4 digit numbers possible - 4!
No of 3 digit numbers possible - 3!
So correct 4 digit numbers is 4! - 3! = 24 - 6 = 18


Could you explain the thought process behind this. Why aren't you subtracting the number of 2 digits possible and number of 1 digits possible.



Question : In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition

We have 4 distinct digits 0,2,4,7 . The different possible 4 digit numbers are

2047,2074,2470,2407,2704,2740
4027,4072,4207,4270,4702,4720
7024,7042,7204,7240,7402,7420 I.e 18 Numbers in all.

An easier way to solve this instead of writing down the numbers would be :

Lets say we have 2 digits say 1,2.
The number of 2 digits numbers possible is 2! ( 12,21)

Lets say we have 3 digits 0,1,2.
The possible number of 3 digits combinations possible is 3! ( 012,021,102,120,210,201 )
But 012 and 021 are not 3 digit numbers right ? They are 2 digit numbers ( 012 is same as 12, 021 is same as 21)
Hence the correct number of 3 digit numbers possible are 3! - 2 or (3! - 2!)

In the original question we have 4 distinct digits 0,2,4,7.
The possible no of 4 digit combination is 4! , but this includes combinations such as 0247,0274 etc,... which we need to subtract from 4!.
To find combinations such as 0274,0247.... we need to start the combination with 0 and the other 3 digits can be placed in any order.
0(2,4,7) - Number of ways to do this is 3!

Hence the num of 4 digits number possible is 4! - 3! = 18.

We don't have to subtract 2 digit or 1 digit number because we are not counting them.
Example : 2 digits number 24 or 47 are not part of our Initial possible set of numbers(4!) :

2047,2074,2470,2407,2704,2740
4027,4072,4207,4270,4702,4720
7024,7042,7204,7240,7402,7420
0247,0274,0427,0472,0724,0742

Hope this helps.
_________________

Consistency is the Key

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1546
Premium Member CAT Tests
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 25 Sep 2017, 08:49
fitzpratik wrote:
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition

A. 12

B. 24

C. 18

D. 4

E. 28

Using FCP:

____ * ____ * ____ * ____

Conditions: 1) must be a 4-digit number; and 2) numbers from which to choose, no repetition: (0, 2, 4, 7)

First slot can be 2, 4 or 7 - there are three possibilities

_3_

Second slot also has only three possibilities; once 2, 4, or 7 is chosen, there are three numbers left

_3_ * _3_

Then, third slot, there are two numbers that remain as possibilities. Fourth slot: one possible number.

_3_ * _3_ * _2_ * _1_

=\(18\)

Answer C
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)
Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]

Show Tags

New post 25 Sep 2017, 18:03
fitzpratik wrote:
In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition

A. 12

B. 24

C. 18

D. 4

E. 28


Since the first digit of any number can’t be 0, there are 3 choices for the first digit. Since no digits can be repeated, the number of choices for the second, third, and fourth digits will be 3, 2, and 1, respectively. Thus, the number of ways a 4-digit number can be formed is 3 x 3 x 2 x 1 = 18.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit   [#permalink] 25 Sep 2017, 18:03
Display posts from previous: Sort by

In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.