Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Oct 2014, 04:15

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many 4 digit numbers are there, if it is known that the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 02 Nov 2009
Posts: 21
Followers: 0

Kudos [?]: 15 [0], given: 9

How many 4 digit numbers are there, if it is known that the [#permalink] New post 28 Jan 2010, 14:45
12
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (02:30) correct 60% (02:03) wrong based on 167 sessions
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

A. 20
B. 150
C. 225
D. 300
E. 320
[Reveal] Spoiler: OA
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23393
Followers: 3608

Kudos [?]: 28820 [7] , given: 2852

Re: Problem Solving [#permalink] New post 28 Jan 2010, 15:19
7
This post received
KUDOS
Expert's post
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
A. 20
B. 150
C. 225
D. 300
E. 320

4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.

Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320

Numbers with two 2-s, 2X2X 1*5*1*4=20.

Thus there are 320-20=300 such numbers.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

3 KUDOS received
Manager
Manager
User avatar
Joined: 08 Apr 2012
Posts: 129
Followers: 10

Kudos [?]: 60 [3] , given: 14

Re: How many 4 digit numbers are there [#permalink] New post 31 May 2012, 00:23
3
This post received
KUDOS
Joy111 wrote:
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

A)20
B)150
C)225
D)300
E)320


Hi,

The first digit can be 2, 4, 6, 8.
The second digit can be 1, 3, 5, 7, 9
The third digit can be 2, 3, 5, 7
The fourth digit can be 0, 3, 6, 9

Case 1: Using 2 as the 1st digit only.

The first digit can be 2, 4, 6, 8. No. of selections = 4
The second digit can be 1, 3, 5, 7, 9. No. of selections = 5
The third digit can be 3, 5, 7. No. of selections = 3
The fourth digit can be 0, 3, 6, 9. No. of selections = 4

Total number of numbers = 4x5x3x4 = 240

Case 2: Using 2 as the 3rd digit only.

The first digit can be 4, 6, 8. No. of selections = 3
The second digit can be 1, 3, 5, 7, 9. No. of selections = 5
The third digit can be 2. No. of selections = 1
The fourth digit can be 0, 3, 6, 9. No. of selections = 4

Total number of numbers = 3x5x1x4 = 60

Hence, total number of numbers = 240 + 60 = 300

Answer is D.

Regards,

Shouvik.
_________________

Shouvik
http://www.Edvento.com
admin@edvento.com

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 11 Dec 2012
Posts: 313
Followers: 59

Kudos [?]: 191 [1] , given: 66

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 17 Jul 2013, 09:04
1
This post received
KUDOS
Expert's post
Since this has been solved a few times (all correctly), I'd like to spend a minute looking at the answer choices. This type of question is very hard to backsolve, but it's relatively easy to see where the trap answers lie.

How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

A. 20
B. 150
C. 225
D. 300
E. 320

The correct answer is D, but if you neglect the restriction of 2 being used twice, the total number of options is E: 320. If you go the other way and over-emphasize this restriction, you end up with answer choice A: 20. C is the choice if you forget that zero is also a multiple of 3 (classic GMAT trap). You'd then have 3/4 as many choices and would get to C. B is a little harder to get to without making multiple mistakes, but it may be a fairly tempting number if you're guessing blindly.

It's obviously crucial to determine which answer choice is the correct one, but there is value in analyzing the other choices and seeing where the GMAT thinks your brain may go. Remember this exam is nothing if not foreseeable and preparable.

Hope this helps!
-Ron
_________________

Ron Awad
Veritas Prep | GMAT Instructor
Save $100 on Veritas Prep GMAT Courses and Admissions Consulting Services
Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 77 [0], given: 6

Re: Problem Solving [#permalink] New post 30 Jan 2010, 07:07
Bunuel wrote:
sudai wrote:
Hi All,

Need your help in solving the below problem!

How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

The answer is 300, but why....

Thank you very much!!


4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.

Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320

Numbers with two 2-s, 2X2X 1*5*1*4=20.

Thus there are 320-20=300 such numbers.


Why do we have to consider 0 for the last digit? Shouldn't it be only 3,6, and 9 ?

Please explain.

Cheers
Intern
Intern
avatar
Joined: 02 Nov 2009
Posts: 21
Followers: 0

Kudos [?]: 15 [0], given: 9

Re: Problem Solving [#permalink] New post 30 Jan 2010, 09:40
Because 0 is divisible by 3.
Manager
Manager
avatar
Joined: 12 May 2012
Posts: 83
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GMAT 3: Q V
GPA: 4
WE: General Management (Transportation)
Followers: 2

Kudos [?]: 44 [0], given: 14

Re: Problem Solving [#permalink] New post 31 May 2012, 03:03
cipher wrote:

Why do we have to consider 0 for the last digit? Shouldn't it be only 3,6, and 9 ?

Please explain.

Cheers


I missed the '0' :(

hope to remember it in future
Intern
Intern
avatar
Joined: 19 Apr 2012
Posts: 28
Followers: 0

Kudos [?]: 2 [0], given: 8

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 25 Jul 2012, 09:56
"4 options for the first digit: 2, 4, 6, 8;"

Aren't there 5 options ? 0 is even as far as know and so meets also the condition ?
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [0], given: 43

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 25 Jul 2012, 11:24
Trying to save some time...

For the second digit, 5 possibilities: 1, 3, 5, 7, 9
For the last (fourth) digit, 4 possibilities: 0, 3, 6, 9

Therefore, the total number of possibilities should be a multiple of 20 = 5 * 4.
A is out, being too small, there are more possibilities for the first and the third digit.

So, I have to chose between D and E.

First digit, 4 possibilities: 2, 4, 6, 8
Third digit also 4 possibilities: 2, 3, 5, 7

It would give 4 * 4 = 16, and 16 * 20 = 320, but because we have to allow only one digit of 2, the final number should be less than 320.
Only 300 is left.

Well, I guess being lazy to carry out all the computations it isn't always safe, but sometimes it feels so good to take even a little shortcut...
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 16 Apr 2012
Posts: 8
Followers: 0

Kudos [?]: 8 [0], given: 3

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 26 Jul 2012, 03:40
Alexmsi wrote:
"4 options for the first digit: 2, 4, 6, 8;"

Aren't there 5 options ? 0 is even as far as know and so meets also the condition ?


0 is even indeed.
But if you take 0 for your first digit, it means you have a 3digits number and we are looking for a 4 digits number.
Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 23 [0], given: 16

Re: Problem Solving [#permalink] New post 26 Jul 2012, 07:22
Bunuel wrote:
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
A. 20
B. 150
C. 225
D. 300
E. 320

4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.

Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320

Numbers with two 2-s, 2X2X 1*5*1*4=20.

Thus there are 320-20=300 such numbers.

Answer: D.


Hello Bunuel, can you please help me understand how u calculated for the restriction?
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Intern
Intern
avatar
Joined: 15 Apr 2012
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: Problem Solving [#permalink] New post 05 Aug 2012, 09:19
harshavmrg wrote:
Bunuel wrote:
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
A. 20
B. 150
C. 225
D. 300
E. 320

4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.

Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320

Numbers with two 2-s, 2X2X 1*5*1*4=20.

Thus there are 320-20=300 such numbers.

Answer: D.


Hello Bunuel, can you please help me understand how u calculated for the restriction?



Restriction where the 4 digit number has two twos.
The two 2s can occur in a digit as shown by Bunuel- 2X2X
Therefore number of such numbers 1*5*1*4=20
Hope its clear now.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23393
Followers: 3608

Kudos [?]: 28820 [0], given: 2852

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 16 Jul 2013, 23:38
Expert's post
Senior Manager
Senior Manager
User avatar
Joined: 17 Dec 2012
Posts: 395
Location: India
Followers: 14

Kudos [?]: 192 [0], given: 10

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 16 Jul 2013, 23:58
sudai wrote:
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

A. 20
B. 150
C. 225
D. 300
E. 320


1. first digit is even - 2,4,6,8
2. second digit is odd - 1,3,5,7,9
3. third is prime - 2,3,5,7
4. fourth is divisible by 3- 0,3,6,9

In addition to the above 4 conditions we have the following:
digit 2 can be used only once

Assume two in (1) and (3) are both not used
the number of possibilities is 3*5*3*4=180
In addition to this either the two in (1) or the two in (3) is used
Number of possibilities if the two in (1) is used - 1*5*3*4=60
Number of possibilities if the two in (3) is used - 3*5*1*4=60
total number of possibilities= 180+60+60=300
_________________

Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravna.com

Classroom Courses in Chennai
Online and Correspondence Courses

Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 17 Jul 2013, 07:45
Funny how this is a 700 level question...not much to it really.

Scenario #1: Start with a 2 as the first number. This leaves 5,3 and 4 choices respectively for the rest. Total = 60 #'s
Scenario #2: Start with a 2 as the third number. This leaves 3,5 and 4 choices respectively for the rest. Total = 60 #'s
Scenario #3: Remove 2 as an option for the 1st and 3rd numbers. This leaves 3,5,3 and 4 choices respectively for the rest. Total = 180#'s

Add them up....60+60+180 = 300 Total numbers can be formed. (D)
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2831
Followers: 206

Kudos [?]: 42 [0], given: 0

Premium Member
Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 02 Sep 2014, 19:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
User avatar
Joined: 23 Jan 2013
Posts: 149
Followers: 0

Kudos [?]: 13 [0], given: 22

Re: How many 4 digit numbers are there, if it is known that the [#permalink] New post 30 Sep 2014, 06:42
Did

0,2,4,6,8
1,3,5,7,9
2,3,5,7 (removed 2 as condition says)
0,3,6,9

5*5*3*4=300

P.S. GMATprep considers 0 as even integer, so if use Bunuel's approach, the correct answer is 380
Re: How many 4 digit numbers are there, if it is known that the   [#permalink] 30 Sep 2014, 06:42
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic How many 4 digit numbers abhisheksharma85 1 09 Oct 2013, 09:20
22 How many 4-digit numbers can be formed by using the digits 0 tabsang 10 16 Dec 2012, 04:40
How many different 4 digit numbers can be composed of digits Juaz 1 22 May 2007, 23:23
How many 4 digit numbers begin with a digit that is prime gk3.14 4 16 Oct 2006, 21:24
1 How many four digit numbers divisible by 4 can be made with karvid 6 31 Jan 2006, 06:38
Display posts from previous: Sort by

How many 4 digit numbers are there, if it is known that the

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.