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A "complete set" of disks consists of one green disk, one blue disk

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Bunuel
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A "complete set" of disks consists of one green disk, one blue disk [#permalink] New post   30 Jan 2020, 03:35
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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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E
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rajatchopra1994
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Re: A "complete set" of disks consists of one green disk, one blue disk [#permalink] New post   30 Jan 2020, 03:43
The bag contains 12 complete sets of disks
1 complete set with 4 disks and a half complete set with two different colors are out.
So, the bag contains 10 complete sets and two disks of different color

IMO-E
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Re: A "complete set" of disks consists of one green disk, one blue disk [#permalink] New post   30 Jan 2020, 05:04
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Bunuel 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


Solution


    • A complete set of disks contains: 1 green, 1 blue, 1 orange and 1 purple disks
    • A bag contains: 12 green, 12 blue, 12 orange and 12 purple disks
    • So, the number of complete sets of disks in the bag = 12
    • To have maximum number of complete sets intact in the bag:
      o out of 6 disks, 4 disks should be of different colour so that they make one complete set.
      o Remaining 2 should NOT be of same colour, so that these two belongs to another 1 complete set.
Hence, remaining complete sets in the bag \(= 12-2 =10\)
Thus, the correct answer is option E.
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Re: A "complete set" of disks consists of one green disk, one blue disk [#permalink] New post   30 Jan 2020, 08:54
we can do following
step 1 ; take 1 disk of each in order green,blue,orange, purple ; we left with 11 in each bag
step 2; take 1 each from green and blue
left with 10 sets then i.e max possible
IMO E

Bunuel 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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Re: A "complete set" of disks consists of one green disk, one blue disk [#permalink] New post   30 Jan 2020, 12:29
Given that
• 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.

There are 48(12+ 12+ 12+ 12) different colored disks in bag.
If 6 disks are randomly selected, there are 42 disks remaining in bag.
From these 42 disks remaining in bag, maximum 10 complete sets consisting of 4 different colored disks and remaining 2 disks which cannot make any set.
Answer:E
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Re: A "complete set" of disks consists of one green disk, one blue disk [#permalink] New post   05 Feb 2020, 05:32
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Bunuel 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


To maximize the number of complete sets in the bag, we should minimize the number of disks selected of 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.

Answer: E
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Re: A "complete set" of disks consists of one green disk, one blue disk [#permalink]
05 Feb 2020, 05:32
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