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

It is currently 19 Oct 2018, 15:00

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

M07-12

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

Hide Tags

Manager
Manager
User avatar
B
Joined: 09 Aug 2017
Posts: 62
Location: United States
Concentration: Technology
GMAT 1: 640 Q44 V33
GMAT 2: 630 Q47 V29
WE: Research (Investment Banking)
Re: M07-12  [#permalink]

Show Tags

New post 13 Oct 2017, 07:23
Yeah, that looks like a negative sign there. I understand probability can't be negative, but it did take a few seconds of rereading that. Grammatically, you wouldn't put a dash there anyway. It should be a comma.
_________________

I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

Also, I appreciate any kudos.

Intern
Intern
avatar
B
Joined: 11 Oct 2017
Posts: 1
Re M07-12  [#permalink]

Show Tags

New post 20 Dec 2017, 21:59
I think this is a high-quality question and I agree with explanation.
Intern
Intern
User avatar
B
Joined: 11 Apr 2016
Posts: 7
WE: Information Technology (Telecommunications)
Premium Member
Re M07-12  [#permalink]

Show Tags

New post 03 Apr 2018, 21:03
I think this the explanation isn't clear enough, please elaborate. As I thought that if of Ben looses the championship that means either Mike or Rob has won so I chose 6/7.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: M07-12  [#permalink]

Show Tags

New post 03 Apr 2018, 21:57
himalayanmonk wrote:
I think this the explanation isn't clear enough, please elaborate. As I thought that if of Ben looses the championship that means either Mike or Rob has won so I chose 6/7.


You can check more solutions here: https://gmatclub.com/forum/if-ben-were- ... 11216.html

Hope it helps.
_________________

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
avatar
G
Joined: 26 Dec 2017
Posts: 152
Premium Member Reviews Badge
Re: M07-12  [#permalink]

Show Tags

New post 11 Jul 2018, 20:04
Bunuel wrote:
Official Solution:

If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\) . If the probability of Ben being the winner is \(\frac{1}{7}\), what is the probability that either Mike or Rob will win the championship? Assume that there can be only one winner.

A. \(\frac{1}{12}\)
B. \(\frac{1}{7}\)
C. \(\frac{1}{2}\)
D. \(\frac{7}{12}\)
E. \(\frac{6}{7}\)


This is a conditional probability question. We need the probability that either Mike or Rob will win the championship. So Ben must lose: the probability of Ben losing is \(1-\frac{1}{7}=\frac{6}{7}\).

Now out of these \(\frac{6}{7}\) cases the probability of Mike winning is \(\frac{1}{4}\) and the probability of Rob winning is \(\frac{1}{3}\). So \(P=\frac{6}{7}(\frac{1}{4}+\frac{1}{3})=\frac{1}{2}\).

Or consider the following:

Take 84 championships/cases (I chose 84 as it's a LCM of 3, 4, and 7).

Now, out of these 84 cases Ben will lose in \(\frac{6}{7}*84=72\). Mike would be the winner in \(72*\frac{1}{4}=18\) (1/4 th of the cases when Ben loses) and Rob would be the winner in \(72*\frac{1}{3}=24\). Therefore \(P=\frac{18+24}{84}=\frac{1}{2}\).


Answer: C

If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\)
I interpreted the red marked area as
Probability(B(not win))*P(M(win))=1/4
Probability(B(not win))*P(R(win))=1/3

Any one pls help me understand the above sentence the significance of "If Ben were to lose the championship"
_________________

--If you like my post pls give kudos

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
M07-12  [#permalink]

Show Tags

New post 11 Jul 2018, 20:53
tejyr wrote:
Bunuel wrote:
Official Solution:

If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\) . If the probability of Ben being the winner is \(\frac{1}{7}\), what is the probability that either Mike or Rob will win the championship? Assume that there can be only one winner.

A. \(\frac{1}{12}\)
B. \(\frac{1}{7}\)
C. \(\frac{1}{2}\)
D. \(\frac{7}{12}\)
E. \(\frac{6}{7}\)


This is a conditional probability question. We need the probability that either Mike or Rob will win the championship. So Ben must lose: the probability of Ben losing is \(1-\frac{1}{7}=\frac{6}{7}\).

Now out of these \(\frac{6}{7}\) cases the probability of Mike winning is \(\frac{1}{4}\) and the probability of Rob winning is \(\frac{1}{3}\). So \(P=\frac{6}{7}(\frac{1}{4}+\frac{1}{3})=\frac{1}{2}\).

Or consider the following:

Take 84 championships/cases (I chose 84 as it's a LCM of 3, 4, and 7).

Now, out of these 84 cases Ben will lose in \(\frac{6}{7}*84=72\). Mike would be the winner in \(72*\frac{1}{4}=18\) (1/4 th of the cases when Ben loses) and Rob would be the winner in \(72*\frac{1}{3}=24\). Therefore \(P=\frac{18+24}{84}=\frac{1}{2}\).


Answer: C

If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\)
I interpreted the red marked area as
Probability(B(not win))*P(M(win))=1/4
Probability(B(not win))*P(R(win))=1/3

Any one pls help me understand the above sentence the significance of "If Ben were to lose the championship"


That sentence means that IF Ben loses, then the probability of Mike winning is 1/4 and IF Ben loses, then the probability of Ron winning is 1/3:
Mike wining = 6/7*1/4
Rob winning = 6/7*1/3

Mike or Rob wining = 6/7*1/4 + 6/7*1/3
_________________

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
avatar
G
Joined: 26 Dec 2017
Posts: 152
Premium Member Reviews Badge
Re: M07-12  [#permalink]

Show Tags

New post 15 Jul 2018, 19:53
1
Bunuel wrote:
tejyr wrote:
Bunuel wrote:
Official Solution:

If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\) . If the probability of Ben being the winner is \(\frac{1}{7}\), what is the probability that either Mike or Rob will win the championship? Assume that there can be only one winner.

A. \(\frac{1}{12}\)
B. \(\frac{1}{7}\)
C. \(\frac{1}{2}\)
D. \(\frac{7}{12}\)
E. \(\frac{6}{7}\)


This is a conditional probability question. We need the probability that either Mike or Rob will win the championship. So Ben must lose: the probability of Ben losing is \(1-\frac{1}{7}=\frac{6}{7}\).

Now out of these \(\frac{6}{7}\) cases the probability of Mike winning is \(\frac{1}{4}\) and the probability of Rob winning is \(\frac{1}{3}\). So \(P=\frac{6}{7}(\frac{1}{4}+\frac{1}{3})=\frac{1}{2}\).

Or consider the following:

Take 84 championships/cases (I chose 84 as it's a LCM of 3, 4, and 7).

Now, out of these 84 cases Ben will lose in \(\frac{6}{7}*84=72\). Mike would be the winner in \(72*\frac{1}{4}=18\) (1/4 th of the cases when Ben loses) and Rob would be the winner in \(72*\frac{1}{3}=24\). Therefore \(P=\frac{18+24}{84}=\frac{1}{2}\).


Answer: C

If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\)
I interpreted the red marked area as
Probability(B(not win))*P(M(win))=1/4
Probability(B(not win))*P(R(win))=1/3

Any one pls help me understand the above sentence the significance of "If Ben were to lose the championship"


That sentence means that IF Ben loses, then the probability of Mike winning is 1/4 and IF Ben loses, then the probability of Ron winning is 1/3:
Mike wining = 7/6*1/4
Rob winning = 7/6*1/3

Mike or Rob wining = 7/6*1/4 + 7/6*1/3


Hi,
Thank you for your reply.
I did not get why Mike=7/6*1/4
and why not Mike=6/7*1/4 (Probability(mike win)*Prob(Ben lose))
Can you pls explain.
_________________

--If you like my post pls give kudos

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: M07-12  [#permalink]

Show Tags

New post 15 Jul 2018, 20:28
tejyr wrote:
Bunuel wrote:
tejyr wrote:
If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\)
I interpreted the red marked area as
Probability(B(not win))*P(M(win))=1/4
Probability(B(not win))*P(R(win))=1/3

Any one pls help me understand the above sentence the significance of "If Ben were to lose the championship"


That sentence means that IF Ben loses, then the probability of Mike winning is 1/4 and IF Ben loses, then the probability of Ron winning is 1/3:
Mike wining = 7/6*1/4
Rob winning = 7/6*1/3

Mike or Rob wining = 7/6*1/4 + 7/6*1/3


Hi,
Thank you for your reply.
I did not get why Mike=7/6*1/4
and why not Mike=6/7*1/4 (Probability(mike win)*Prob(Ben lose))
Can you pls explain.


It's a typo there. Of course it's 6/7 in both cases. The probability cannot be more than 1.
_________________

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
User avatar
B
Joined: 23 Jan 2018
Posts: 18
Re: M07-12  [#permalink]

Show Tags

New post 03 Aug 2018, 10:10
Bunuel
Are we not considering the probability(1-1/3) of Rob losing the game when we are taking the winning probability of Mike since Mike's winning probability already include all the possibilities, even that of Rob losing the game?
Is my thinking correct?
_________________

"Winning is all about right strategy"

Set S.M.A.R.T Objectives : Specific | Measurable | Attainable | Relevant | Time-Bound

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: M07-12  [#permalink]

Show Tags

New post 03 Aug 2018, 10:28
Setback wrote:
Bunuel
Are we not considering the probability(1-1/3) of Rob losing the game when we are taking the winning probability of Mike since Mike's winning probability already include all the possibilities, even that of Rob losing the game?
Is my thinking correct?


We are told that there can be only one winner. So, if Mike wins, Rob looses and if Rob wins, Mike looses (automatically).
_________________

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

Senior Manager
Senior Manager
User avatar
P
Joined: 04 Jun 2018
Posts: 280
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
Premium Member Reviews Badge CAT Tests
Re: M07-12  [#permalink]

Show Tags

New post 09 Aug 2018, 13:42
Bunuel wrote:
dyg wrote:
Hello,

I think question should be edited bcs it seems like Rob's probability of winning is -1/3. Minus should be eliminated from the question.


Probability cannot be negative, so it's clearly a dash a not a minus sign.


While I am aware that probability cannot be negative, I was briefly thrown off by the dash as well.
_________________

A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated! :)

Intern
Intern
avatar
B
Joined: 14 Aug 2017
Posts: 14
GMAT ToolKit User CAT Tests
Re: M07-12  [#permalink]

Show Tags

New post 04 Sep 2018, 22:50
Hi Bunuel,

I understood the official solution. But I have a doubt in the wording of the question, although I landed up with the correct answer , but I wanted to get it confirmed from you.

According to the question " If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob - 1/3 ", I thought that since only one person can win at at time , P(Mike winning) = 1/4 and P(Rob Losing) = 1/3 are given, so then
P(Rob Winning) = 1- P(Rob Losing)= 1-(1/3) =2/3
and P(Ben Winning) = 1/7, which is already given . So P(Ben Losing) = 1 - P(Ben Winning) = 1-(1/7)= 6/7
Now we have to calculate the probability of winning of either Mike or Rob ,

P(Mike Win) = P(Ben Losing)*P(Mike Winning)*P(Rob Losing) = (6/7)*(1/4)*(1/3)=1/14
P(Rob Win) = P(Ben Losing)*P(Mike Losing)*P(Rob Winning) = (6/7)*(3/4)*(2/3)=3/7

P(Mike Win or Rob Win) = P(Mike Win) + P(Rob Win) = (1/14)+(3/7) = 1/2

The final answer is same i.,e 1/2 . But my interpretation was different as compared to official explanation.
So I wanted to get it confirmed from you. Whether my approach/understanding is correct?

Thanks
GMAT Club Bot
Re: M07-12 &nbs [#permalink] 04 Sep 2018, 22:50

Go to page   Previous    1   2   [ 32 posts ] 

Display posts from previous: Sort by

M07-12

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

Moderators: chetan2u, Bunuel



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®.