For a school outing, the school has 20 small ice chests, each of which

really a good question
total bottles which can be accomodated; 20*6; 120
10 chests are full so we have 60 bottles
now we need to fill all the 20 chests with atleast 1 can and no more than 6
so 4 cans in a box can be accomodated in 60/4 ; 15 boxes
or say 13*4; +1*6 +2*1 ; 52+6+2 ; 60
so we can have 13 chests with 4 cans each
IMO C

abhishekdadarwal2009 according to your solution total chests would be 21 but there are 20 chests ..

Hi Thanks for noticing,
Updated the post.

C:13 best answer in 13*4=52, left=8 then each of the 6 chests have 1 can left and one chest will have 2 cans.

Each of the small ice chests can hold a maximum of six cans of soda. There are 20 such chests. Therefore, the maximum number of soda cans that can be stored in these chests is 120.

10 of the ice chests are full, which means that there are 60 cans. We need to rearrange these cans such that each chest must have at least one soda can and every soda can should be there in a chest.

To maximize the number of chests that have exactly four cans, let’s start with the biggest number given in the options, which is option E.

If 15 chests have four cans each, it means that 5 cans do not have any cans at all. This violates the condition given in the question. So, option E is not the right answer.

Let’s look at option D. If 14 chests have four cans each, 56 cans out of 60 are in these 14 chests. The remaining 4 cans can be accommodated in 4 chests, but 2 chests will still be empty. Option D cannot be the right answer.

If 13 cans have four cans each, that’s 52 cans. We are left with 8 cans and 7 chests. Clearly, we can arrange so that every chest has at least one can. Therefore, option C has to be the right answer.

The most important point that needs to be realized here, is that the 60 cans are going to be rearranged among all the 20 cans, satisfying certain conditions. The moment you understand this part, is when you start getting closer to the right answer.

Hope this helps!

We see that there are a total of 6 x 10 = 60 cans. If 15 ice chests have 4 cans each, then we have 5 empty ice chests left. However, since each ice chest must have at least one can, we see that we can’t have 15 ice chests with 4 cans each.

Let’s say 14 ice chests have 4 cans each; then we have a total of 56 cans in these 14 ice chests. We see that we have 4 cans left but 6 ice chests left. So we would still have at least 2 empty ice chests. So it’s impossible to have 14 ice chests with 4 cans each.

Let’s say 13 ice chests have 4 cans each, so we have a total of 52 cans in these 13 ice chests. We see that we have 8 cans left but 7 ice chests left. So we can have 6 ice chests with 1 can each and the last ice chest with 2 cans. We see that it’s possible to have 13 ice chests with 4 cans each. Therefore, the largest number of ice chests that can have exactly four cans is 13.

Answer: C

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