It is currently 24 Feb 2018, 11:47

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

Brian plays a game in which two fair, six-sided dice are rol

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

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 02 Mar 2013
Posts: 9
Reviews Badge
Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 07:52
1
This post received
KUDOS
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

35% (01:39) correct 65% (01:33) wrong based on 192 sessions

HideShow timer Statistics

Brian plays a game in which two fair, six-sided dice are rolled simultaneously. For each die, an even number means that he wins that amount of money and an odd number means that he loses that amount of money. What is the probability that Brian makes money on his first roll?

A. 11/12
B. 7/12
C. 1/2
D. 5/12
E. 1/3
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jun 2014, 07:55, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 08:50
Expert's post
7
This post was
BOOKMARKED
sidinsin wrote:
Brian plays a game in which two fair, six-sided dice are rolled simultaneously. For each die, an even number means that he wins that amount of money and an odd number means that he loses that amount of money. What is the probability that Brian makes money on his first roll?

A. 11/12
B. 7/12
C. 1/2
D. 5/12
E. 1/3


Brian will win in cases when both dice show an even number as well as in cases when an odd number on one die is less than an even number on another.

A. An even number on both dice can occur in 3*3 = 9 cases.

B. An odd number on one die is less than an even number on another:

(1, 2) and (2, 1)

(1, 4) and (4, 1)

(1, 6) and (6, 1)

(3, 4) and (4, 3)

(3, 6) and (6, 3)

(5, 6) and (6, 5)

12 cases here.

P = favorable/total = (9 + 12)/36 = 7/12.

Answer: C.
_________________

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

Intern
Intern
avatar
Joined: 28 Mar 2014
Posts: 23
Location: India
GPA: 3
WE: Business Development (Retail Banking)
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 08:59
What does 'die' means here?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 09:04
Intern
Intern
avatar
Joined: 02 Mar 2013
Posts: 9
Reviews Badge
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 09:14
Hi Bunuel
Could you clarify, "Brian will win in cases when both dice show an even number as well as in cases when an odd number on one die is less than an even number on another."

The question stem does not say anything about the odd number has to be less than the even number. IMO, the winning combinations are:

1.) e-e: 3/6*3/6
2) o-e
1,2:1,4:1:6
3,2: 3,4: 3,6
5,2: 5,4: 5,6

Winning prb: 3/6*3/6+ (9/36)*2= 1/4+ 1/2= 3/4

Thanks
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 09:19
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
sidinsin wrote:
Hi Bunuel
Could you clarify, "Brian will win in cases when both dice show an even number as well as in cases when an odd number on one die is less than an even number on another."

The question stem does not say anything about the odd number has to be less than the even number. IMO, the winning combinations are:

1.) e-e: 3/6*3/6
2) o-e
1,2:1,4:1:6
3,2: 3,4: 3,6
5,2: 5,4: 5,6

Winning prb: 3/6*3/6+ (9/36)*2= 1/4+ 1/2= 3/4

Thanks


For each die, an even number means that he wins that amount of money and an odd number means that he loses that amount of money.

So, for example:
In case of (2=even, 4=even) he wins 2 + 4 = $6.
In case of (2=even, 5=odd) he losses 2 - 5 = $3.
In case of (6=even, 1=odd) he wins 6 - 1 = $5.

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 02 Mar 2013
Posts: 9
Reviews Badge
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 18 Jun 2014, 09:24
Thanks make sense. Need to read the stem more carefully.
Expert Post
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 394
Location: India
GMAT 1: 760 Q50 V44
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 01 Oct 2015, 04:03
1
This post received
KUDOS
Expert's post
This is an interesting question and needs you to read the question stem attentively.
We are sure that Brian will win in the case when there is an even number and loose the same amount if there is an odd number.

Bifurcating the cases.

1. Brian will win some money if there are even numbers on both the dices.
2. Brian will win some money if the even number on one die is more than the odd number. Here Brian will win the money equal to the difference of the two numbers on the dices.

Case 1:
Even numbers on both dices.
Since there are 3 even numbers on a dice: 2, 4, 6
This is possible in 3*3 = 9 ways

Case 2:
Even number is greater the odd number
This is possible in the following ways
(2, 1), (4, 1),(4, 3), (6, 1), (6, 3), (6, 5)
These numbers can be interchanged on both the dices.
Hence a total of 12 cases.

Total outcomes = 6*6 = 36
Probability = 12+9/36 = 21/36 = 7/12

Option B.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: Brian plays a game in which two fair, six-sided dice are rol [#permalink]

Show Tags

New post 30 Dec 2017, 00:46
sidinsin wrote:
Brian plays a game in which two fair, six-sided dice are rolled simultaneously. For each die, an even number means that he wins that amount of money and an odd number means that he loses that amount of money. What is the probability that Brian makes money on his first roll?

A. 11/12
B. 7/12
C. 1/2
D. 5/12
E. 1/3


VERITAS PREP OFFICIAL SOLUTION:


First, consider how Brian can win or lose: two even numbers guarantee a win, while two odd numbers guarantee a loss. If he gets one odd and one even, he wins money if the even is greater than the odd and loses money if the odd is greater than the even. If he rolls a 6, he can roll any odd number and still make money. If he rolls a 4, then odd must be 1 or 3, and if he rolls a 2, then the odd must be 1. The probability of making money is then:

Even AND even: 3/6 * 3/6 = 9/36 = 1/4

One even, one odd:

6 AND any odd: 1/6 * 3/6 = 3/36

Any odd AND 6: 3/6 * 1/6 = 3/36

4 AND 1 or 3: 1/6 * 2/6 = 2/36

1 or 3 AND 4: 2/6 * 1/6 = 2/36

2 AND 1: 1/6 * 1/6 = 1/36

1 AND 2: 1/6 * 1/6 = 1/36

Total = 12/36 = 1/3

The probability of making money is then 1/4 + 1/3, or 7/12.
_________________

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

Re: Brian plays a game in which two fair, six-sided dice are rol   [#permalink] 30 Dec 2017, 00:46
Display posts from previous: Sort by

Brian plays a game in which two fair, six-sided dice are rol

  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®.