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Register now and save up to $200 Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code ## A certain bag of gemstones is composed of two-thirds... tagged by: LUANDATO This topic has 2 expert replies and 0 member replies ### Top Member LUANDATO Master | Next Rank: 500 Posts Joined 15 Oct 2017 Posted: 323 messages Followed by: 1 members #### A certain bag of gemstones is composed of two-thirds... Thu Dec 07, 2017 11:07 am 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 DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2542 messages Followed by: 116 members Upvotes: 1153 GMAT Score: 770 Thu Dec 07, 2017 11:22 am 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

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### GMAT/MBA Expert

DavidG@VeritasPrep Legendary Member
Joined
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Thu Dec 07, 2017 11:19 am
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

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