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

It is currently 22 Sep 2018, 17:55

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

A barrel contains only red balls, white balls, and brown balls. If two

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

Hide Tags

Intern
Intern
avatar
Joined: 05 Feb 2014
Posts: 43
A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post Updated on: 24 Oct 2017, 21:59
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

72% (01:00) correct 28% (00:46) wrong based on 235 sessions

HideShow timer Statistics

A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is \(\frac{2}{3}\)

(2) There are nine balls in the barrel.

Originally posted by gauravsoni on 20 May 2014, 12:39.
Last edited by Bunuel on 24 Oct 2017, 21:59, edited 3 times in total.
Edited the question.
Intern
Intern
avatar
Joined: 17 May 2014
Posts: 40
Re: A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post 20 May 2014, 20:47
2
gauravsoni wrote:
A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is .

(2) There are nine balls in the barrel.




This is an interesting one. The question says we have only red, white and brown balls. And we have to find the probability that both balls drawn with replacement are brown.

Probability of getting 1 brown ball = number of brown balls/ total number of balls = A

Probability that both balls drawn are brown = A.A = A^2. (Note that A is dependent on number of brown balls and total number of balls which are 2 variables)

Statement 1: The probability that one ball selected at random is either red or white is 2/3.

This means probability of not getting a brown ball =2/3
Therefore, A which is probability of getting a brown ball is 1/3

Now since, we want to get A^2, it may seem that we can answer the question. But this is a trap. Lets say, we have only 3 balls. A=1/3 means, we have only 1 brown ball. Thus, probability of getting 2 brown balls become 0. In case it is more than 3 balls, i.e. 6, 9, 12, ans so on, we can predict the probability.
Hence, this is insufficient

Statement 2: There are nine balls in the barrel.

We don't know the number of brown balls and hence can't predict the probability.

Hence insufficient.

Now, let us take both the statement together. After statement 1, if we can assure that the barrel has more than 3 balls, we can definitely tell the probability. Now, we are given 9 balls. Which means we can calculate the probability.

Hence, answer is C.

Hope it helps!!

Kudos if you like!!
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 698
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post 20 May 2014, 21:41
1
gauravsoni wrote:
A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is \(\frac{2}{3}\)

(2) There are nine balls in the barrel.


Can someone please explain the working ?



Let there be x red balls, y, white balls and z brown balls .

From st 1 we have that the probability of selection either red or white is 2/3

or (x+y)/ (x+y+z)= 2/3 -----We see that x+y=2z or total no. of balls =3z

So probability of drawing 2 brown balls will be \(zc2/3zc2\) or z(z-1)/(3z-1)*(3z-2)------Thus till we know z we can find the probability

St 2 says that x+y+z=9 so not sufficient

Combining we see that 3z=9 and z=3 so probability will be 3/9 or 1/3.

Ans is C.....
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post 21 May 2014, 02:27
1
A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is \(\frac{2}{3}\). This implies that 1/3rd of the balls in the barrel are brown. If there are only 3 balls in the barrel then the probability of selecting two brown balls is obviously 0 but if there are say 6 balls in the barrel then the probability of selecting two brown balls is greater than 0. Not sufficient.

(2) There are nine balls in the barrel. Clearly insufficient.

(1)+(2) 1/3*9=3 balls out of 9 are brown. We can get the probability. Sufficient.

Answer: C.

Remember, on DS problems, all you need to do is evaluate whether you would be able to arrive at the answer using the information provided in each statement; you don’t need to waste time actually finding the answer.
_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post 21 May 2014, 02:36
WoundedTiger wrote:
gauravsoni wrote:
A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is \(\frac{2}{3}\)

(2) There are nine balls in the barrel.


Can someone please explain the working ?



Let there be x red balls, y, white balls and z brown balls .

From st 1 we have that the probability of selection either red or white is 2/3

or (x+y)/ (x+y+z)= 2/3 -----We see that x+y=2z or total no. of balls =3z

So probability of drawing 2 brown balls will be \(zc2/3zc2\) or z(z-1)/(3z-1)*(3z-2)------Thus till we know z we can find the probability

St 2 says that x+y+z=9 so not sufficient

Combining we see that 3z=9 and z=3 so probability will be 3/9 or 1/3.

Ans is C.....


We have 3 brown balls out of 9. The probability of selecting 2 brown balls is 3/9*2/8 = 1/12.
_________________

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

GMATH Teacher
User avatar
B
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 197
A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post 29 Aug 2018, 12:23
gauravsoni wrote:
A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is \(\frac{2}{3}\)

(2) There are nine balls in the barrel.


\(?\,\,\,\, = \,\,\,P\left( {2\,\,br\,\,{\text{out}}\,\,{\text{of}}\,\,2\,\,{\text{sequential}}\,\,{\text{extractions}}\,\,{\text{no}}\,\,{\text{replacements}}} \right)\,\,\)

\(\left( 1 \right)\,\,P\left( {re\,\,{\text{or}}\,\,wh\,\,{\text{out}}\,\,{\text{of}}\,\,1\,\,{\text{extraction}}} \right) = \frac{2}{3}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,P\left( {br\,\,{\text{out}}\,\,{\text{of}}\,\,1\,\,{\text{extraction}}} \right) = \frac{1}{3}\)

\(\left\{ \begin{gathered}
\,{\text{Take}}\,\,\,\left( {r,w,b} \right) = \left( {1,1,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0 \hfill \\
\,{\text{Take}}\,\,\,\left( {r,w,b} \right) = \left( {2,2,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? \ne 0 \hfill \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,\,r + w + b\,\, = \,\,9\)

\(\left\{ \begin{gathered}
\,{\text{Take}}\,\,\,\left( {r,w,b} \right) = \left( {7,1,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0 \hfill \\
\,{\text{Take}}\,\,\,\left( {r,w,b} \right) = \left( {6,1,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? \ne 0 \hfill \\
\end{gathered} \right.\)

\(\left( {1 + 2} \right)\,\,\,br = \frac{1}{3}\left( 9 \right) = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\, = \,\,{\text{unique}}\,\,\,\,\left( {\frac{3}{9} \cdot \frac{2}{8}} \right)\)

The above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: A barrel contains only red balls, white balls, and brown balls. If two  [#permalink]

Show Tags

New post 05 Sep 2018, 10:54
1
gauravsoni wrote:
A barrel contains only red balls, white balls, and brown balls. If two balls are selected at random without replacing each ball, what is the probability that two brown balls will be selected?

(1) The probability that one ball selected at random is either red or white is \(\frac{2}{3}\)

(2) There are nine balls in the barrel.


Statement One Alone:

The probability that one ball selected at random is either red of white is 2/3.

That means the probability that one ball selected at random is brown is 1/3. However, since we don’t know how many brown balls there are, we can’t determine the probability that two brown balls will be selected without replacement. For example, if there are 2 brown balls in the barrel (before any selection), the probability that two brown balls will be selected without replacement is 2/6 x 1/5 = 1/3 x 1/5 = 1/15. However, if there are 3 brown balls in the barrel (before any selection), the probability that two brown balls will be selected without replacement is 3/9 x 2/8 = 1/3 x 1/4 = 1/12.

Statement one alone is not sufficient.

Statement Two Alone:

There are nine balls in the barrel.

Without knowing the number of balls of each color (especially the color brown) or the probability of selecting a certain color (especially the color brown), we can’t determine the probability that two brown balls will be selected without replacement.

Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we can determine that there are 3 brown balls in the barrel (before any selection) since 1/3 x 9 = 3. Knowing that there are 3 brown balls in the barrel (before any selection), we can also determine the probability that two brown balls will be selected without replacement. That probability is is 3/9 x 2/8 = 1/3 x 1/4 = 1/12.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

GMAT Club Bot
Re: A barrel contains only red balls, white balls, and brown balls. If two &nbs [#permalink] 05 Sep 2018, 10:54
Display posts from previous: Sort by

A barrel contains only red balls, white balls, and brown balls. If two

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

Events & Promotions

PREV
NEXT


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®.