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A number of 50 marbles is to be divided and contain wit

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A number of 50 marbles is to be divided and contain wit [#permalink]

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A number of 50 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 17
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 14 Feb 2011, 16:09
banksy wrote:
A number of 50 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 17


To maximize # of boxes we should minimize marbles per box: 15*3+1*5=50 --> 15+1=16.

Answer: D.
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 14 Feb 2011, 16:30
so if it is written that:"each box is to contain 3, 4, or 5 marbles" so it does not mean that there must be at least 1 box with 3 marbles, at least one box with 4 marbles and at least one box with 5 marbles?who to see it in task?cos I thought that it is important to have all kinds of boxes....
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 14 Feb 2011, 16:42
banksy wrote:
so if it is written that:"each box is to contain 3, 4, or 5 marbles" so it does not mean that there must be at least 1 box with 3 marbles, at least one box with 4 marbles and at least one box with 5 marbles?who to see it in task?cos I thought that it is important to have all kinds of boxes....


Don't think that the question means that (though I do find the wording a bit ambiguous which rises the question of the source by the way).
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 14 Feb 2011, 17:40
Bunuel wrote:
banksy wrote:
so if it is written that:"each box is to contain 3, 4, or 5 marbles" so it does not mean that there must be at least 1 box with 3 marbles, at least one box with 4 marbles and at least one box with 5 marbles?who to see it in task?cos I thought that it is important to have all kinds of boxes....


Don't think that the question means that (though I do find the wording a bit ambiguous which rises the question of the source by the way).


that was what i thought as well.

I figured there must be one of each type of box.

3*12=36
4*1=4
5*2=10

15 boxes...total 50 marbles filling each type of box.
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 06 Mar 2018, 10:05
Bunuel why are we taking 15 boxes and 1 box for 3 and 5 respectively

Why did we omit 4 ?
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 06 Mar 2018, 10:19
rohail786911 wrote:
Bunuel why are we taking 15 boxes and 1 box for 3 and 5 respectively

Why did we omit 4 ?


We want a. to maximize the number of boxes and b. to distribute all 50 marbles.

If we put 3 marbles in 15 3-marble boxes, we'll be left with 5 marbles, which we can put in 5-marble box. In this case we'll use 15*3 + 1*5 = 50 --> 15 + 1 = 16 boxes.

We could get the same maximum also in another way: put 3 marbles in 14 3-marble boxes, we'll be left with 8 marbles, and distribute these 8 into two 4-marble boxes. In this case we'll still use 14*3 + 2*5 = 50 --> 14 + 2 = 16 boxes.

For more on this topic:

14. Min/Max Problems



For other topics check:
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Hope it helps.
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 07 Mar 2018, 03:10
The number of boxes can be maximized only if the maximum number of the balls go into the box with capacity "3". 50=16*3+2 (remaining number cant be accommodated anywhere)...50=15*3+5 {the remaining 5 balls can be accommodated in the box with capacity 5}. Therefore, the largest possible number of boxes = 15 {capacity 3} +0 { capacity 4} + 1 {capacity 5} = 16.


banksy wrote:
A number of 50 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 17
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Re: A number of 50 marbles is to be divided and contain wit [#permalink]

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New post 08 Mar 2018, 17:56
banksy wrote:
A number of 50 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 17


In order to get the largest number of boxes, we want to maximize the number of boxes that contain 3 marbles.

Thus, we can have 3 x 15 boxes = 45 marbles and then 1 box that contains 5 marbles, resulting in a total of 16 boxes as the max.

Answer: D
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Re: A number of 50 marbles is to be divided and contain wit   [#permalink] 08 Mar 2018, 17:56
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