• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote A certain bag of gemstones is composed of two-thirds... tagged by: BTGmoderatorLU This topic has 2 expert replies and 0 member replies Top Member A certain bag of gemstones is composed of two-thirds... 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 The OA is C. I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced. GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2666 messages Followed by: 125 members Upvotes: 1153 GMAT Score: 770 Top Reply DavidG@VeritasPrep wrote: LUANDATO 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 The OA is C. I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced. We're told that there are twice as many diamonds as rubies in this bag, so let's designate the number of diamonds as '2x' and the number of rubies as 'x,' giving us a total of 3x. Probability that the first pick is a diamond = # diamonds/# tot gems = 2x/3x Probability that the second pick is also a diamond given that the first pick was a diamond = (2x -1)/(3x -1) Probability that the two picks are diamonds = (2x/3x) * (2x -1)/(3x -1) = 5/12 (2/3) * (2x -1)/(3x -1) = 5/12 (4x - 2)/(9x -3) = 5/12 48x -24 = 45x - 15 3x = 9 x = 3 So we've got 2x = 2*3 = 6 diamonds, x = 3 rubies and 9 total gems. We want the probability of selecting two rubies. Probability that first pick is a ruby = 3/9 Probability that second pick is a ruby given that first pick was a ruby = 2/8 Probability that both picks are rubies = (3/9)(2/8) = 6/72 = 1/12. The answer is C Note that you could also skip the algebra and just play with scenarios. If we know that there are twice as many diamonds as rubies, we can try: Scenario One: 2 diamonds and 1 ruby. P(selecting two diamonds) = (2/3)(1/2) = 2/6 --> not 5/12 Scenario Two: 4 diamonds and 2 rubies. P(selecting two diamonds) = (4/6)(3/5) = 12/30 --> not 5/12 Scenario Three: 6 diamonds and 3 rubies. P(selecting two diamonds) = (6/9)(5/8) = 30/72 = 5/12. Perfect! So we know there are 6 diamonds and 3 rubies. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2666 messages
Followed by:
125 members
1153
GMAT Score:
770
LUANDATO 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

The OA is C.

I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.
We're told that there are twice as many diamonds as rubies in this bag, so let's designate the number of diamonds as '2x' and the number of rubies as 'x,' giving us a total of 3x.

Probability that the first pick is a diamond = # diamonds/# tot gems = 2x/3x
Probability that the second pick is also a diamond given that the first pick was a diamond = (2x -1)/(3x -1)
Probability that the two picks are diamonds = (2x/3x) * (2x -1)/(3x -1) = 5/12
(2/3) * (2x -1)/(3x -1) = 5/12
(4x - 2)/(9x -3) = 5/12
48x -24 = 45x - 15
3x = 9
x = 3

So we've got 2x = 2*3 = 6 diamonds, x = 3 rubies and 9 total gems.

We want the probability of selecting two rubies.
Probability that first pick is a ruby = 3/9
Probability that second pick is a ruby given that first pick was a ruby = 2/8
Probability that both picks are rubies = (3/9)(2/8) = 6/72 = 1/12. The answer is C

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 32 first replies
5 GMATGuruNY 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

159 posts
2 Max@Math Revolution

Math Revolution

92 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

60 posts
4 Ian Stewart

GMATiX Teacher

50 posts
5 GMATGuruNY

The Princeton Review Teacher

37 posts
See More Top Beat The GMAT Experts