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Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr

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Magoosh GMAT Instructor
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Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 02 Feb 2015, 17:44
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Difficulty:

  95% (hard)

Question Stats:

44% (01:32) correct 56% (02:52) wrong based on 61 sessions

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Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720


The GMAT loves tricky counting problems such as this. For a discussion of how to approach such problems, with the OE to this particular problem, see:
https://magoosh.com/gmat/2015/counting- ... -the-gmat/

Mike :-)

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Mike McGarry
Magoosh Test Prep

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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 05 Feb 2015, 14:48
mikemcgarry wrote:
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720


The GMAT loves tricky counting problems such as this. For a discussion of how to approach such problems, with the OE to this particular problem, see:
https://magoosh.com/gmat/2015/counting- ... -the-gmat/

Mike :-)


Hey Mike,

The OA here is different from the one posted on the Magoosh link. I got 90, which is the OA here, but the site says 180.
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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 05 Feb 2015, 14:57
1
aviram wrote:
mikemcgarry wrote:
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720


The GMAT loves tricky counting problems such as this. For a discussion of how to approach such problems, with the OE to this particular problem, see:
https://magoosh.com/gmat/2015/counting- ... -the-gmat/

Mike :-)


Hey Mike,

The OA here is different from the one posted on the Magoosh link. I got 90, which is the OA here, but the site says 180.

Dear aviram,
My friend, be careful. On the Magoosh site, there are two questions, #8 and #9, that superficially look identical, but there's a subtle different makes the answers different. The question posted here in this GC thread is #9, which indeed has the OA you calculated, but when you looked at the Magoosh website, I believe you looked at the OA of #8.
You never can read too carefully on the GMAT Quant section. Does all this make sense?
Mike :-)
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Mike McGarry
Magoosh Test Prep

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Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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Joined: 27 Jun 2014
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GMAT 1: 710 Q43 V45
GRE 1: Q161 V163

GRE 2: Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 05 Feb 2015, 23:10
mikemcgarry wrote:
aviram wrote:
mikemcgarry wrote:
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720


The GMAT loves tricky counting problems such as this. For a discussion of how to approach such problems, with the OE to this particular problem, see:
https://magoosh.com/gmat/2015/counting- ... -the-gmat/

Mike :-)


Hey Mike,

The OA here is different from the one posted on the Magoosh link. I got 90, which is the OA here, but the site says 180.

Dear aviram,
My friend, be careful. On the Magoosh site, there are two questions, #8 and #9, that superficially look identical, but there's a subtle different makes the answers different. The question posted here in this GC thread is #9, which indeed has the OA you calculated, but when you looked at the Magoosh website, I believe you looked at the OA of #8.
You never can read too carefully on the GMAT Quant section. Does all this make sense?
Mike :-)



Whatever you say makes sense to me dear Mike :)
_________________

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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 19 Mar 2015, 13:30
I tried this:

3 Blue Marble:

Different distribution : (1) All 3 in the same cup (2) Split 2-1 in two cups (3) Split 1-1-1

Case (1) 3 possibilities
Case (2) 6 possibilities ,
Case (3) 1 possibility

tot. 10 possibilities.

One Green Marble :

3 possibilities (one for each cup at the time)

First Red marble:

3 possibilities (one for each cup at the time)

Second Red marble:

2 possibilities ( because can't go in the same cup with the other Red marble)

TOTAL:

10*3*3*2 = 180 , answer, B .

Let me know if my conclusion is correct. thanks!
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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 20 Mar 2015, 03:57
mikemcgarry wrote:
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720


The GMAT loves tricky counting problems such as this. For a discussion of how to approach such problems, with the OE to this particular problem, see:
https://magoosh.com/gmat/2015/counting- ... -the-gmat/

Mike :-)



blue --> 3,0,0 ==> 3!/2! ; 2,1,0 ==> 3! ; 1,1,1 ==> 3!/3!
total = (3+6+1) = 10

red --> 1,1,0 ==> 3!/2! = 3

green --> 1,0,0 = 3!/2! = 3

answer = 10*3*3 = 90.
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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr  [#permalink]

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New post 20 Dec 2017, 05:06
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Re: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr &nbs [#permalink] 20 Dec 2017, 05:06
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