This question came from kaplan..
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
What formula is this? I'm hoping for mathmatical equation to understand this! thanks,
[spoiler]OA-e
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.[/spoiler][/spoiler]
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
What formula is this? I'm hoping for mathmatical equation to understand this! thanks,
[spoiler]OA-e
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.[/spoiler][/spoiler]
