Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 09:53

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A certain bag of gemstones is composed of two-thirds

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Director
Director
avatar
Joined: 13 Nov 2003
Posts: 801
Location: BULGARIA
Followers: 1

Kudos [?]: 18 [3] , given: 0

GMAT Tests User
A certain bag of gemstones is composed of two-thirds [#permalink] New post 29 May 2006, 06:32
3
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (02:45) correct 44% (02:09) wrong based on 104 sessions
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4
[Reveal] Spoiler: OA
1 KUDOS received
Intern
Intern
avatar
Joined: 05 Apr 2006
Posts: 36
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: Challenge MHTNGMAT [#permalink] New post 29 May 2006, 08:03
1
This post received
KUDOS
BG wrote:
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4


is answer 1/12

2/3 * (2X-1) / (3X-1) = 5/ 12 => X = 3
So total gems = 9
and probability of ruby = 1/3 * 2/8 = 1/12
2 KUDOS received
VP
VP
User avatar
Joined: 29 Dec 2005
Posts: 1351
Followers: 6

Kudos [?]: 27 [2] , given: 0

GMAT Tests User
Re: Challenge MHTNGMAT [#permalink] New post 29 May 2006, 08:46
2
This post received
KUDOS
guptaraja wrote:
BG wrote:
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4


is answer 1/12

2/3 * (2X-1) / (3X-1) = 5/ 12 => X = 3
So total gems = 9
and probability of ruby = 1/3 * 2/8 = 1/12


this is good enough.........

[{2/3(x)}/x] [{(2x/3)-1}/x-1] = 5/12
x^2-9x = 0
x = 0, 9

so x = 9
diamond = 6
ruby = 3
the prob (2 ruby) = 3c2/9c2 = 1/12

C.
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Final Lap
Joined: 25 Oct 2012
Posts: 290
Concentration: General Management, Entrepreneurship
Schools: Oxford
GPA: 3.54
WE: Project Management (Retail Banking)
Followers: 2

Kudos [?]: 86 [1] , given: 85

Re: A certain bag of gemstones is composed of two-thirds [#permalink] New post 06 Feb 2013, 16:38
1
This post received
KUDOS
BG wrote:
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4


Let R be the numbers of rubies in the bag,
we told that the selection is made without replacement in both cases ( selecting two diamonds or selecting two rubies)

Hence, we have : \frac{2}{3}*\frac{2R-1}{3R-1}=\frac{5}{12}

So, the number of diamonds in the bag is 6. Likewise, the number of rubies in the bag is 3 and the total of the gemstones is 9.

The probability of selecting two rubies from the bag without replacement is :

\frac{1}{3}*\frac{2}{8}=\frac{1}{12}

Answer : C
_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"


Last edited by Rock750 on 09 Feb 2013, 18:23, edited 1 time in total.
Manager
Manager
avatar
Joined: 08 Dec 2012
Posts: 64
Location: United Kingdom
GMAT 1: 710 Q0 V0
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 43 [0], given: 31

Re: A certain bag of gemstones is composed of two-thirds [#permalink] New post 09 Feb 2013, 18:13
Rock750 wrote:
BG wrote:
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4


Let R be the numbers of rubies in the bag,
we told that the selection is made without replacement in both cases ( selecting two diamonds or selecting two rubies)

Hence, we have : \frac{2}{3}*\frac{2R-1}{3R-1}=\frac{5}{12}

So, the number of diamonds in the bag is 3. Likewise, the number of rubies in the bag is 6 and the total of the gemstones is 9.

The probability of selecting two rubies from the bag without replacement is :

\frac{1}{3}*\frac{2}{8}=\frac{1}{12}

Answer : C



Looks like you got your diamonds and rubies mixed up :wink: though you got it right later
Senior Manager
Senior Manager
User avatar
Status: Final Lap
Joined: 25 Oct 2012
Posts: 290
Concentration: General Management, Entrepreneurship
Schools: Oxford
GPA: 3.54
WE: Project Management (Retail Banking)
Followers: 2

Kudos [?]: 86 [0], given: 85

Re: A certain bag of gemstones is composed of two-thirds [#permalink] New post 09 Feb 2013, 18:28
nave81 wrote:
Rock750 wrote:
BG wrote:
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4


Let R be the numbers of rubies in the bag,
we told that the selection is made without replacement in both cases ( selecting two diamonds or selecting two rubies)

Hence, we have : \frac{2}{3}*\frac{2R-1}{3R-1}=\frac{5}{12}

So, the number of diamonds in the bag is 3. Likewise, the number of rubies in the bag is 6 and the total of the gemstones is 9.

The probability of selecting two rubies from the bag without replacement is :

\frac{1}{3}*\frac{2}{8}=\frac{1}{12}

Answer : C



Looks like you got your diamonds and rubies mixed up :wink: though you got it right later



u are right navy81, thx :)

Hope this silly mistake had not confused anyone. Anyway, i think it's OK by now :-D
_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"

1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 10

Kudos [?]: 138 [1] , given: 254

GMAT ToolKit User
Re: A certain bag of gemstones is composed of two-thirds [#permalink] New post 09 Jan 2014, 14:00
1
This post received
KUDOS
BG wrote:
A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4


(d/d+r)(d-1/d+r-1) = 5/12

d = 2r

Therefore r = 3
d= 6

Probability of 2 rubies is

(3/9)(2/8) = 1/12

C it is
Intern
Intern
avatar
Joined: 29 Aug 2013
Posts: 12
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: A certain bag of gemstones is composed of two-thirds [#permalink] New post 09 Jan 2014, 14:27
Can someone explain the

2/3 * (2R-1)/(3R-1)

part?
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4598
Location: Pune, India
Followers: 1043

Kudos [?]: 4559 [1] , given: 162

Re: A certain bag of gemstones is composed of two-thirds [#permalink] New post 09 Jan 2014, 20:55
1
This post received
KUDOS
Expert's post
b00gigi wrote:
Can someone explain the

2/3 * (2R-1)/(3R-1)

part?


Say, a bag has 6 diamonds and 3 rubies. What is the probability of selecting 2 diamonds one after the other without replacement?

Probability of selecting one diamond = 6/9
Probability of selecting yet another diamond after selecting one = 5/8 (no of diamonds has gone down by 1 and total no. of diamonds has gone down by 1 too)
Total probability = (6/9)*(5/8)

Here, we assume that no of rubies is R and no of diamonds is 2R (since no of diamonds is twice the no of rubies)
Probability of selecting two diamonds without replacement = (2R/3R) * (2R - 1)/(3R - 1) = 5/12
Either cross multiply to get the value of R or try to plug in some values to see where you get a multiple of 12 in the denominator.
Once you get the value of R as 3, you know the number of diamonds is 6.

Probability of picking two rubies one after the other without replacement = (3/9) *(2/8) = 1/12
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: A certain bag of gemstones is composed of two-thirds   [#permalink] 09 Jan 2014, 20:55
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic A certain bag of gem stones is composed of 2/3 diamonds and prateekbhatt 3 10 Aug 2013, 08:39
8 Experts publish their posts in the topic Certain gemstones are formed by magma, a material found deep iwillcrackgmat 16 12 Mar 2012, 01:30
10 Experts publish their posts in the topic A certain panel is to be composed of exactly three women and mariyea 22 09 Feb 2011, 13:05
In a certain packinghouse, grapefruit are packed in bags and tarek99 3 06 Jan 2008, 23:11
A certain panel is to be composed of exactly three women and iamba 2 16 Jul 2007, 17:13
Display posts from previous: Sort by

A certain bag of gemstones is composed of two-thirds

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.