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

It is currently 01 Sep 2015, 22:26
GMAT Club Tests

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

A box contains 100 tickets marked 1 to 100. One ticket is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Director
Director
avatar
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 42 [1] , given: 7

A box contains 100 tickets marked 1 to 100. One ticket is [#permalink] New post 07 Feb 2011, 01:33
1
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

60% (02:14) correct 40% (02:52) wrong based on 15 sessions
A box contains 100 tickets marked 1 to 100. One ticket is picked at random. What is the probability that the number on the ticket will be divisible by either 2 or 3, but not 6?

The official answer is:

[Reveal] Spoiler:
51/100


The official solution is the following:

[Reveal] Spoiler:
All possibilities = 100
Numbers divisible by 2 = 50 ... A
Numbers divisible by 3 = 33 ... B
Numbers divisible by 6 = 16 ... C

Positive outcomes = A + B - 2*C

Probability = 51/100


Can someone please explain why they subtract C twice?

Thank you.

Last edited by Bunuel on 07 Jul 2013, 04:43, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29185
Followers: 4736

Kudos [?]: 50053 [3] , given: 7525

Re: Box with 100 tickets marked 1...100 [#permalink] New post 07 Feb 2011, 02:24
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
nonameee wrote:
The question from a textbook on probability:

A box contains 100 tickets marked 1 to 100. One ticket is picked at random. What is the probability that the number on the ticket will be divisible by either 2 or 3, but not 6?

The official answer is:

[Reveal] Spoiler:
51/100


The official solution is the following:

[Reveal] Spoiler:
All possibilities = 100
Numbers divisible by 2 = 50 ... A
Numbers divisible by 3 = 33 ... B
Numbers divisible by 6 = 16 ... C

Positive outcomes = A + B - 2*C

Probability = 51/100


Can someone please explain why they subtract C twice?

Thank you.


A box contains 100 tickets marked 1 to 100. One ticket is picked at random. What is the probability that the number on the ticket will be divisible by either 2 or 3, but not 6?

Total = 100 numbers.

Numbers divisible by 2 = 50 ... A
Numbers divisible by 3 = 33 ... B
Numbers divisible by 6 = 16 ... C

Now, both A (numbers divisible by 2) and B (numbers divisible by 3) contain C (numbers divisible by 6) so to get the numbers which are divisible by either 2 or 3, but not 6 we should subtract C twice, once for A and once for B: A + B - 2*C= 51

Probability = 51/100

If it were: "What is the probability that the number on the ticket will be divisible by either 2 or 3 (or both)?" Then we would subtract C only once to get rid of double counting.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 42 [0], given: 7

Re: Box with 100 tickets marked 1...100 [#permalink] New post 07 Feb 2011, 03:12
Bunuel, thanks. I got it.
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2027
Followers: 142

Kudos [?]: 1215 [0], given: 376

Re: Box with 100 tickets marked 1...100 [#permalink] New post 07 Feb 2011, 05:09
I thought it to be 67/100 and realized my mistake.

Count of numbers divisible by 2 = 50. In these 50 numbers there are 16 numbers that are divisible by 6 and we must take them out. 50-16=34

Count of numbers divisible by 3 = 33. In these 33 numbers there are 16 numbers that are divisible by 6 and we must take them out. 33-16=17

Total numbers divisible by 2 or 3 but not 6 = 34+17=51

Probability = 51/100.

Good one.
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
User avatar
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 659
Followers: 37

Kudos [?]: 434 [0], given: 39

Re: Box with 100 tickets marked 1...100 [#permalink] New post 08 Feb 2011, 11:11
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 32

Kudos [?]: 344 [0], given: 355

GMAT ToolKit User
Re: A box contains 100 tickets marked 1 to 100. One ticket is [#permalink] New post 25 Nov 2013, 07:26
nonameee wrote:
A box contains 100 tickets marked 1 to 100. One ticket is picked at random. What is the probability that the number on the ticket will be divisible by either 2 or 3, but not 6?

The official answer is:

[Reveal] Spoiler:
51/100


The official solution is the following:

[Reveal] Spoiler:
All possibilities = 100
Numbers divisible by 2 = 50 ... A
Numbers divisible by 3 = 33 ... B
Numbers divisible by 6 = 16 ... C

Positive outcomes = A + B - 2*C

Probability = 51/100


Can someone please explain why they subtract C twice?

Thank you.


Every 6 numbers there are 3 divisible by 2 or 3 and not divisible by 6
Then in 100 numbers there are 16 sets of 6 and 4 numbers left as remainder.
So, 16(3) = 48. Now of the numbers remaining (92,98,99 and 100) there 3 of them are multiples of 2 or 3 but not 6.
So total is 51 numbers
Hence prob is 51/100

Hope it helps
Cheers
J :)
Intern
Intern
avatar
Joined: 13 Dec 2013
Posts: 40
Schools: Fuqua (I), AGSM '16
GMAT 1: 620 Q42 V33
Followers: 2

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

GMAT ToolKit User
Re: A box contains 100 tickets marked 1 to 100. One ticket is [#permalink] New post 01 Jun 2014, 07:59
Is it the same as saying: divisible by either 2 or 3 but not by both?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29185
Followers: 4736

Kudos [?]: 50053 [0], given: 7525

Re: A box contains 100 tickets marked 1 to 100. One ticket is [#permalink] New post 01 Jun 2014, 08:49
Expert's post
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6168
Followers: 344

Kudos [?]: 70 [0], given: 0

Premium Member
Re: A box contains 100 tickets marked 1 to 100. One ticket is [#permalink] New post 14 Jul 2015, 05:55
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

Re: A box contains 100 tickets marked 1 to 100. One ticket is   [#permalink] 14 Jul 2015, 05:55
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic A box contain a certain number of balls, marked successively from 1 to Turkish 4 26 Feb 2015, 16:32
3 Experts publish their posts in the topic A theater box office sold an average of 65 tickets per staff Gnpth 3 08 Jul 2014, 06:29
A bag contains 30 tickets devinawilliam83 5 19 Dec 2011, 11:16
Tickets Madelaine88 0 03 Mar 2011, 11:43
27 Experts publish their posts in the topic A box contains 100 balls, numbered from 1 to 100. If three b SmitKhurana 19 13 Feb 2011, 10:46
Display posts from previous: Sort by

A box contains 100 tickets marked 1 to 100. One ticket is

  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®.