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

 It is currently 02 Aug 2015, 05:20

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain bag of gemstones is composed of two-thirds

Author Message
TAGS:
Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

Kudos [?]: 30 [4] , given: 0

A certain bag of gemstones is composed of two-thirds [#permalink]  29 May 2006, 06:32
4
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

59% (03:06) correct 41% (02:16) wrong based on 187 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
Intern
Joined: 05 Apr 2006
Posts: 36
Followers: 0

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

Re: Challenge MHTNGMAT [#permalink]  29 May 2006, 08:03
1
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

2/3 * (2X-1) / (3X-1) = 5/ 12 => X = 3
So total gems = 9
and probability of ruby = 1/3 * 2/8 = 1/12
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 7

Kudos [?]: 38 [2] , given: 0

Re: Challenge MHTNGMAT [#permalink]  29 May 2006, 08:46
2
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

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.
Senior Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 294
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Followers: 3

Kudos [?]: 159 [1] , given: 85

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  06 Feb 2013, 16:38
1
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 :

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

_________________

KUDOS is the good manner to help the entire community.

Last edited by Rock750 on 09 Feb 2013, 18:23, edited 1 time in total.
Manager
Joined: 08 Dec 2012
Posts: 67
Location: United Kingdom
GMAT 1: 710 Q0 V0
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 74 [0], given: 31

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  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 :

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

Looks like you got your diamonds and rubies mixed up though you got it right later
Senior Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 294
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Followers: 3

Kudos [?]: 159 [0], given: 85

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  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 :

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

Looks like you got your diamonds and rubies mixed up 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
_________________

KUDOS is the good manner to help the entire community.

SVP
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 30

Kudos [?]: 324 [2] , given: 355

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  09 Jan 2014, 14:00
2
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
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]  09 Jan 2014, 14:27
Can someone explain the

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

part?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5746
Location: Pune, India
Followers: 1446

Kudos [?]: 7604 [1] , given: 186

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  09 Jan 2014, 20:55
1
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

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 5712
Followers: 323

Kudos [?]: 63 [0], given: 0

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  03 Feb 2015, 08:56
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 3078
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 134

Kudos [?]: 852 [0], given: 54

Re: A certain bag of gemstones is composed of two-thirds [#permalink]  03 Feb 2015, 21:53
Expert's post
Hi All,

We can solve this problem by TESTing VALUES. However, we have so much specific information, we CANNOT TEST random values. We have to use the information in the prompt to pick a logical number that matches all of the given "restrictions"

Here's what we have to work with:
1) Since the gems can be broken down into 2/3 diamonds and 1/3 rubies, the TOTAL must be a MULTIPLE of 3.
2) Since the probability of pulling 2 diamonds is 5/12, when we multiply the two individual probabilities, we MUST end with a denominator that is a multiple of 12 (so the fraction can be reduced to 5/12).

Let's start at "3" and work up....

If there are 3 gems, then we have 2 diamonds.
The probability of pulling 2 diamonds is (2/3)(1/2) = 2/6 which is NOT a match.

If there are 6 gems, then we have 4 diamonds.
The probability of pulling 2 diamonds is (4/6)(3/5) = 12/30.....30 cannot reduce to 12. This is NOT a match

If there are 9 gems, then we have 6 diamonds.
The probability of pulling 2 diamonds is (6/9)(5/8) = 5/12...This IS a MATCH

So we have....
Total= 9
Diamonds = 6
Rubies = 3

The question asks for the probability of selecting 2 rubies....

The probability of selecting the first ruby = (3/9)
The probability of selecting the second ruby = (2/8)
(3/9)(2/8) = 6/72 = 1/12

[Reveal] Spoiler:
C

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

Re: A certain bag of gemstones is composed of two-thirds   [#permalink] 03 Feb 2015, 21:53
Similar topics Replies Last post
Similar
Topics:
6 A certain bag contains 60 balls —22 white, 18 green, 11 yellow, 5 red, 5 11 May 2015, 06:27
6 A certain bag of gem stones is composed of 2/3 diamonds and 3 10 Aug 2013, 08:39
19 In a certain game, a large bag is filled with blue, green 20 22 Jan 2012, 16:24
1 Candles and Bags 3 13 Jul 2010, 19:42
10 In a certain game, a large bag is filled with blue, green, p 16 26 Jan 2010, 04:41
Display posts from previous: Sort by