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

It is currently 10 Dec 2018, 00:44

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

A box contains red and blue balls only. If there are 8 balls

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

Hide Tags

Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 117
Reviews Badge
A box contains red and blue balls only. If there are 8 balls  [#permalink]

Show Tags

New post 27 Nov 2010, 19:36
1
5
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

60% (01:14) correct 40% (01:37) wrong based on 182 sessions

HideShow timer Statistics

A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Please explain your appraoch
Manager
Manager
User avatar
Status: I rest, I rust.
Joined: 04 Oct 2010
Posts: 99
Schools: ISB - Co 2013
WE 1: IT Professional since 2006
Re: Balls in the box  [#permalink]

Show Tags

New post 27 Nov 2010, 20:01
2
1
udaymathapati wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Please explain your appraoch

Lets say there are R red balls and 8-R blue balls.
S1: P(Both-Red) = \(\frac{R}{8}*\frac{R-1}{7} = \frac{5}{14}\)
so R(R-1) = 5*4, hence R = 5 (considering only positive value). Sufficient

S2: P(Red-Blue) = \(\frac{R}{8}*\frac{8-R}{7} = \frac{15}{56}\)
so R(8-R) = 15, hence R = 5 or 3. Not Sufficient

Answer: A
_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

Senior Manager
Senior Manager
avatar
P
Joined: 17 Mar 2014
Posts: 378
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: A box contains red and blue balls only. If there are 8 balls  [#permalink]

Show Tags

New post 28 Aug 2018, 16:49
udaymathapati wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Please explain your appraoch


I was able to deduce statement 1 to \(R(R-1)/8*7\) and statement 2 to \(R(8-R)=15\). I didn't solve it further as I thought R can be calculated but end up getting it wrong :P

I chose D as answer. :(
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7095
A box contains red and blue balls only. If there are 8 balls  [#permalink]

Show Tags

New post 28 Aug 2018, 17:39
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
Let the number of red balla be R and blue balla be B

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
if there are R red balls , the first can be picked in R ways and the next in R-1 ways
Therefore probability = \(\frac{R}{8}*\frac{R-1}{8-1}=\frac{5}{14}.......R(R-1)=\frac{8*7*5}{14}=5*4\)
Thus R =5
Sufficient

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.
Probability = \(\frac{R}{8}*\frac{B}{8-1}=\frac{15}{56}.......R*B=\frac{8*7*15}{56}=15=5*3\)
5*3 is the only possibility as 5+3=8 but R could be 3 or 5
Insufficient

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Senior Manager
Senior Manager
avatar
P
Joined: 17 Mar 2014
Posts: 378
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: A box contains red and blue balls only. If there are 8 balls  [#permalink]

Show Tags

New post 28 Aug 2018, 18:57
1
chetan2u wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
Let the number of red balla be R and blue balla be B

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
if there are R red balls , the first can be picked in R ways and the next in R-1 ways
Therefore probability = \(\frac{R}{8}*\frac{R-1}{8-1}=\frac{5}{14}.......R(R-1)=\frac{8*7*5}{14}=5*4\)
Thus R =5
Sufficient

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.
Probability = \(\frac{R}{8}*\frac{B}{8-1}=\frac{15}{56}.......R*B=\frac{8*7*15}{56}=15=5*3\)
5*3 is the only possibility as 5+3=8
Sufficient

D


chetan2u,
u also made same mistake which I made. Only statement 1 is sufficient. Statement 2 gives, two values for R=3,5.
Answer should be A.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7095
Re: A box contains red and blue balls only. If there are 8 balls  [#permalink]

Show Tags

New post 28 Aug 2018, 19:05
ammuseeru wrote:
chetan2u wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
Let the number of red balla be R and blue balla be B

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
if there are R red balls , the first can be picked in R ways and the next in R-1 ways
Therefore probability = \(\frac{R}{8}*\frac{R-1}{8-1}=\frac{5}{14}.......R(R-1)=\frac{8*7*5}{14}=5*4\)
Thus R =5
Sufficient

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.
Probability = \(\frac{R}{8}*\frac{B}{8-1}=\frac{15}{56}.......R*B=\frac{8*7*15}{56}=15=5*3\)
5*3 is the only possibility as 5+3=8
Sufficient

D


chetan2u,
u also made same mistake which I made. Only statement 1 is sufficient. Statement 2 gives, two values for R=3,5.
Answer should be A.


Thanks..
I for some reason read Red balls are more than blue although it is not mentioned. May be I had a similar question earlier.

Kudos
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13050
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A box contains red and blue balls only. If there are 8 balls  [#permalink]

Show Tags

New post 29 Nov 2018, 15:42
Hi All,

We're told that a box contains red and blue balls only and that there are 8 balls in total. We're asked for the number of RED balls are in the box.

1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

To start, since we're selecting balls from the box WITHOUT replacement, the probability that the first ball will be red is X/8 (where X is the number of red balls). If we pull a red ball on the first try, then there will be one FEWER red ball for the second try, so the probability of pulling a red ball then is (X-1)/7.

Thus, the overall probability will be (X)(X-1)/(8)(7) = (X)(X-1)/56. The given fraction is 5/14, which has clearly been reduced. 5/14 = 20/56, so we're looking for a value of X such that (X)(X-1) = 20. There's only one positive value that fits here... X= 5 --> since (5)(4) = 20
Fact 1 is SUFFICIENT

2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Based on the work that we did in Fact 1, we can look for a similar pattern in Fact 2. The numerator of 15/56 is '15', so we need two numbers that SUM to 8 (one for the number of red balls and one for the number of blue balls) that when multiplied together give us 15. Those would clearly be 3 and 5. However, we do NOT know which one is which. We could have 3 red balls and 5 blue balls OR 5 red balls and 3 blue balls.
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

GMAT Club Bot
Re: A box contains red and blue balls only. If there are 8 balls &nbs [#permalink] 29 Nov 2018, 15:42
Display posts from previous: Sort by

A box contains red and blue balls only. If there are 8 balls

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


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®.