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# A "complete set" of disks consists of one green disk, one bl

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A "complete set" of disks consists of one green disk, one bl  [#permalink]

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12 Feb 2018, 08:04
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Difficulty:

15% (low)

Question Stats:

77% (01:22) correct 23% (02:01) wrong based on 127 sessions

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A "complete set" of disks consists of one green disk, one blue disk, one orange disk, and one purple disk. A bag contains 12 green disks, 12 blue disks, 12 orange disks, and 12 purple disks. The bag contains nothing else. If 6 disks are randomly selected from the bag, what is the greatest possible number of complete sets of disks that could be remaining in the bag?
A. 5
B. 6
C. 8
D. 9
E. 10

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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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13 Feb 2018, 00:30
there are 12 complete sets

6 discs are removed-----1 disc each from colour-->4
remaining 2 from a colour each

so there are 10 complete sets now
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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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20 Feb 2018, 03:53
Green12-Blue12-Orange12-Purple12
1 - 1 - 1 - 3 (4c3 ways = 4)
1 - 1 - 2 - 2 (4c2 ways = 6)

Total 10.
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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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22 Feb 2018, 09:17
Sasindran wrote:
A "complete set" of disks consists of one green disk, one blue disk, one orange disk, and one purple disk. A bag contains 12 green disks, 12 blue disks, 12 orange disks, and 12 purple disks. The bag contains nothing else. If 6 disks are randomly selected from the bag, what is the greatest possible number of complete sets of disks that could be remaining in the bag?
A. 5
B. 6
C. 8
D. 9
E. 10

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To maximize the number of complete sets in the bag, we should minimize the number of disks selected from each color. Since we are choosing 6 disks and since there are 4 available colors, we should select 2 disks of the same color for 2 colors and 1 disk of each of the remaining colors.

If we removed, for instance, 2 green, 2 blue, 1 orange, and 1 purple disks, the remaining disks would be:

10 green, 10 blue, 11 orange, and 11 purple disks, from which we could make 10 complete sets.

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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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15 Jun 2018, 09:57
Since we have 12 discs in each set and 4 colors and we want the greatest number of sets to be remained in the bag after removing 6, we assume that all removed are of different color, 1 disc of each color and 2 of any other but not the same. we will be left with 10 complete sets (+2 discs of some other colors).
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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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15 Jun 2018, 12:11
E. 10
Must take away at least 2 from 3 colors.
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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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30 Nov 2018, 13:49
In order to solve this problem we must think about how to maximize the number of complete sets of disks that will remain in the bag. If all 6 disks removed are orange, then there will only be 6 orange disks remaining in the bag. Since there will be 12 blue disks, 12 orange disks, and 12 purple disks remaining in the bag, it will only be possible to select 6 complete sets of disks. So to maximize the number of complete sets remaining in the bag, we should remove a complete set consisting of one green disk, one blue disk, one orange disk, and one purple disk, and then 2 more disks that are of different colors. This will leave 10 complete sets of disks in the bag. There will also be 2 additional different disks. Therefore choice (E) is the correct answer.

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Re: A "complete set" of disks consists of one green disk, one bl  [#permalink]

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01 Dec 2018, 04:48

Total number of disks 48

Total number of sets 12

Each set has 4 disks

So 4 disks taken from one set, and 2 more from the second set

So we are left with 10 remaining complete sets

YAY
Re: A "complete set" of disks consists of one green disk, one bl   [#permalink] 01 Dec 2018, 04:48
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