Author 
Message 
TAGS:

Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3479

Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
05 Oct 2012, 09:26
1
This post received KUDOS
8
This post was BOOKMARKED
Question Stats:
57% (03:09) correct 43% (03:22) wrong based on 133 sessions
HideShow timer Statistics
Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no blue paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of blue paint 4) J2, if the paint contains exactly 1 jar of blue paint What is the probability that the new colour will be a shade of J (J1 or J2)? (A) 75/84 (B) 10/21 (C) 17/42 (D) 11/21 (E) 37/42 For me is a good question, maybe time consuming because when you understand what is asked, the question must be setup carefully. Let me know
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Intern
Joined: 04 Dec 2011
Posts: 26

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
05 Oct 2012, 12:21
[/spoiler] carcass wrote: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no blue paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of blue paint 4) J2, if the paint contains exactly 1 jar of blue paint What is the probability that the new colour will be a shade of J (J1 or J2)? (A) 75/84 (B) 10/21 (C) 17/42 (D) 11/21 (E) 37/42 For me is a good question, maybe time consuming because when you understand what is asked, the question must be setup carefully. Let me know Probability of J=Probability of J1 + J2 Probability of J1=((4c2*5c1) + (4c3))/(9c4) atleast 2 so it can be 2 blue or 3 blue solving we get. =(17/42) Probability of J2=(4c1*5c2)/(9c4) solving we get =(20/42) Probability of j=(17/42) + (20/42) =37/42 ans is E



Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
05 Oct 2012, 14:36
11
This post received KUDOS
2
This post was BOOKMARKED
carcass wrote: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no blue paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of blue paint 4) J2, if the paint contains exactly 1 jar of blue paint What is the probability that the new colour will be a shade of J (J1 or J2)? (A) 75/84 (B) 10/21 (C) 17/42 (D) 11/21 (E) 37/42 For me is a good question, maybe time consuming because when you understand what is asked, the question must be setup carefully. Let me know If the new color doesn't contain Blue paint, then it isn't of type J. So, it is much easier to calculate the complementary probability. P(no Blue paint chosen) = (5/9)*(4/8)*(3/7) = 5/42. Therefore, the required probability is 1  5/42 = 37/42. Answer E.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Board of Directors
Joined: 01 Sep 2010
Posts: 3479

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
05 Oct 2012, 15:51



Intern
Joined: 12 Jun 2012
Posts: 40

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
10 Oct 2012, 04:29
1
This post received KUDOS
Using Combinatrix I start the same way as EvaJager What is the probability that the new paint has either 1,2, or 3 parts blue in it. This is equivalent of saying 1probability(no blue) First, how many ways can we choose 3 paints from 9 paints 3C9, 9!/(3!6!)=84 Second how many ways can we make a paint with no blue, or choose 3 paints from the remaining 5 paints 3C5 = 5!/(3!2!) = 10 answer is 1 (10/84) = 74/84. Simplify and you have your answer!
_________________
If you find my post helpful, please GIVE ME SOME KUDOS!



VP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1358
GRE 1: 1540 Q800 V740

Re: Charlie, a painter, has 9 jars of paint…700 Level PS [#permalink]
Show Tags
12 Apr 2013, 20:12
1
This post received KUDOS
Solution 1:Number of ways of making J1 = number of ways of choosing the paints such that there are two blue paints + number of ways of choosing the paints such that there are three blue paints = 4C2 x 5C1 + 4C3 = 34 Number of ways of making J2 = number of ways of choosing the paints such that there is one jar of blue and two jars of any other color = 4C1 x 5C2 = 40 Number of ways of combining three paints to make a color = 9C3 = 84 Number of ways (new color will be a shade of J1 or J2) = n(J1) + n(J2)  n(J1 n J2) = n(J1) + n(J2) as n(J1 n J2) = 0 [either there will be exactly one color of blue or two or more] Therefore probability (new color will be a shade of J1 or J2) = (40+34)/84 = 74/84 = 37/42 Option E Solution 2:Looking at the classifications, we realize straight away that J1 or J2 = number of ways of selecting the paints such that there is at least one blue paint included Therefore probability = 1  prob. (no blue paint is included) = 1  (5C3/9C3) = 1  10/84 = 74/84 = 37/42 Option E
_________________
GyanOne  Top MBA Rankings and MBA Admissions Blog
Top MBA Admissions Consulting  Top MiM Admissions Consulting
Premium MBA Essay ReviewBest MBA Interview PreparationExclusive GMAT coaching
Get a FREE Detailed MBA Profile Evaluation  Call us now +91 98998 31738



Intern
Status: London UK GMAT Consultant / Tutor
Joined: 30 Oct 2012
Posts: 48

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
13 Apr 2013, 12:42
Think about it like this: the question is asking for the probability that we have three jars of paint, none of which are blue. Thus, it is basically an "at least" question, which invariably implies 1 (full probability)  (probability of the inverse occurrence). That is, if you want the probability that a coin flipped three times will land on Heads at least once, calculate the probability of landing ONLY ON TAILS (=1/8) and subtract it to find the "at least once" situation. 1  1/8 = 7/8 chance that it will land on Heads at least once. So it is simplest to think about it as asking "what is the probability that the mix will have at least one jar of blue paint in it?" The probability of having no jars of blue paint is (B)(B)(B) = (5/9)(4/8)(3/7), which reduces to 5/42. That is, 1  no blue = 1  (B)(B)(B) = 1  5/42 = 37/42. The answer is E.
_________________
Learn the Top 3 GMAT Arithmetic Techniques with this free PDF guide!
http://yourgmatcoach.com/ditchthearithmetic/
PS have you seen the new GMAT Work and Rates guide? Comes with a free 8video course.
https://yourgmatcoach.podia.com/courses/howtobeatgmatworkandratesproblems



Manager
Status: Build your own dreams,Otherwise some one else will hire you to build there's.
Joined: 30 Apr 2015
Posts: 94
Location: India
Concentration: Finance
GMAT 1: 590 Q45 V26 GMAT 2: 660 Q47 V34
GPA: 3.68

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
15 Feb 2016, 08:48
1
This post was BOOKMARKED
Please let me know where am i going wrong, the probability that it would be J1 or J2 is same as 1()probability that it is C1 or C2 For C13C2(Brown)*2C1(Yellow)=3*2=6 For C23C3(all brown)=1 Total=9C3=84 17/84=77/84 I am confused
_________________
"Follow your heart and realize that your dream is a dream for a reason" Dori Roberts



Manager
Joined: 14 Jul 2014
Posts: 191
Location: United States
GMAT 1: 600 Q48 V27 GMAT 2: 720 Q50 V37
GPA: 3.2

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
25 Apr 2016, 11:50
There are three possibilities of getting J shades.
1. Two Blue and 1 nonblue = 4C2 * 5C1 = 6 * 5 = 30 2. Three blue = 4C3 = 4 3. One Blue and two nonblue = 4C1 * 5C2 = 4 * 10 = 40
Total number of possibilities = 9C3 = 84
(40+4+30)/84 = 74/84.
ANS E.



NonHuman User
Joined: 09 Sep 2013
Posts: 13810

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
21 Oct 2017, 06:19
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



SVP
Joined: 12 Dec 2016
Posts: 1906
Location: United States
GPA: 3.64

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
Show Tags
07 Jan 2018, 21:24
this question comes from Aristotle Prep, a reliable source.




Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y
[#permalink]
07 Jan 2018, 21:24






