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

Question

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

Bunuel · Answer

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

Answer: D.

banksy · Answer

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....

Bunuel · Answer

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).

MKParris · Answer

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.

rohail786911 · Answer

Bunuel why are we taking 15 boxes and 1 box for 3 and 5 respectively

Why did we omit 4 ?

Bunuel · Answer

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 
     Theory   
 Maximizing/Minimizing Strategies on the GMAT - All in One Topic! 
     Questions   
 Worst Case Scenario Questions  
 DS Questions 
 PS Questions

For other topics check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

sandeepkonda · Answer

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

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

JeffTargetTestPrep · Answer

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

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