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# There is a set of beads, each of which is painted either red

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Intern
Joined: 26 Aug 2013
Posts: 11

Kudos [?]: 9 [0], given: 19

There is a set of beads, each of which is painted either red [#permalink]

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30 Aug 2013, 02:06
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Difficulty:

85% (hard)

Question Stats:

48% (02:15) correct 52% (01:43) wrong based on 220 sessions

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There is a set of beads, each of which is painted either red or blue. The beads are split, with each bead being cut in half. Then they are merged, where all the halves are randomly reassembled back into the same number of beads that there were to begin with. This results in r red beads, b blue beads, and p beads that are half red and half blue. Before the split and merge, were there more red beads than blue beads?

(1) after the split and merge, the probability of picking a bead that is only red is less than the probability of picking a bead that is at least half blue.
(2) After the split and merge, the probability of picking a bead that is only blue is greater than the probability of picking a bead that is at least half red.

[Reveal] Spoiler:
Well, I got the answer but it took me so long to solve it.
Can someone help me to solve this kind of questions quicker?
[Reveal] Spoiler: OA

Kudos [?]: 9 [0], given: 19

Intern
Joined: 31 Jan 2013
Posts: 17

Kudos [?]: 56 [1], given: 18

Schools: ISB '15
WE: Consulting (Energy and Utilities)
Re: probability question from Princeton review [#permalink]

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30 Aug 2013, 03:12
1
KUDOS
Consider the Number of Red and Blue beads as R and B respectively and, after splitting, the number of beads as R1,B1 and P(mixed)

We need to prove R>B
From the given information, We could say
R+B = R1+B1+P
Or
R = R1+P/2
B = B1+P/2

1) Given R1<B1+P -
R1<B+P/2 or R1+P/2<B+P
R<B+P - from this equation, there is no way we can interpret about R or B. Hence not Sufficient

2) Given B1>R1+P -
From this we could definitely say B>B1>R1+P
B> (R1+P/2)+P/2
So we can definitely say,
B>R
hence St2 is sufficent to answer the question.

I hope this helps
/SW

Kudos [?]: 56 [1], given: 18

Current Student
Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 740 [0], given: 355

Concentration: Finance
Re: There is a set of beads, each of which is painted either red [#permalink]

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02 Jun 2014, 08:53
I don't get it. Bunuel could you solve alternatively?

Question is to express half/half red and blue balls algebraically

Thanks!
Cheers
J

Kudos [?]: 740 [0], given: 355

Current Student
Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 740 [0], given: 355

Concentration: Finance
Re: There is a set of beads, each of which is painted either red [#permalink]

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02 Jun 2014, 08:53
I don't get it. Bunuel could you solve alternatively?

Question is to express half/half red and blue balls algebraically

Thanks!
Cheers
J

Kudos [?]: 740 [0], given: 355

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 281 [0], given: 0

Re: There is a set of beads, each of which is painted either red [#permalink]

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02 Mar 2016, 05:17
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).

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Re: There is a set of beads, each of which is painted either red [#permalink]

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15 Jun 2017, 03:35
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.
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Intern
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Re: There is a set of beads, each of which is painted either red [#permalink]

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16 Jun 2017, 03:07
I got B right away as the only way the prob of only Blue beads > split Red ones is if there were more blue than red beads.
But can someone help do it algebraically as I'd like to see it efficiently laid out using algebra. Thank you.

Kudos [?]: 65 [0], given: 29

Re: There is a set of beads, each of which is painted either red   [#permalink] 16 Jun 2017, 03:07
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