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A grocer is storing soap boxes in cartons that measure 25

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A grocer is storing soap boxes in cartons that measure 25 [#permalink] New post 03 Apr 2013, 06:33
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Question Stats:

75% (01:54) correct 25% (01:11) wrong based on 40 sessions
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A. 210
B. 252
C. 280
D. 300
E. 420
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Apr 2013, 07:04, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Soap boxes in a carton [#permalink] New post 03 Apr 2013, 06:43
deepri0812 wrote:
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A -210
B - 252
C - 280
D -300
E-420


Area of the box = 25*42*60=63000
Area of one soap = 7*6*5=210
Tot number = \frac{63000}{210}=300

You have to calculate the area of the box, then divide it by the area of one soap, and you ll find the number of soaps that will fit into the box
D
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Re: Soap boxes in a carton [#permalink] New post 03 Apr 2013, 06:52
deepri0812 wrote:
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A -210
B - 252
C - 280
D -300
E-420


Please suggest the method to solve such problems.


Maximum number of soap boxes that can be placed in each carton = Volume of each carton/ volume of each box
= (25*42*60)/(7*6*5)= 300(option D)
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Re: Soap boxes in a carton [#permalink] New post 03 Apr 2013, 07:28
Zarrolou wrote:
deepri0812 wrote:
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A -210
B - 252
C - 280
D -300
E-420


Area of the box = 25*42*60=63000
Area of one soap = 7*6*5=210
Tot number = \frac{63000}{210}=300

You have to calculate the area of the box, then divide it by the area of one soap, and you ll find the number of soaps that will fit into the box
D


Thanks Zarrolou for quick reply.

I am getting confused between volume approach as done by you and my thought process:

Think about lining up the dimensions of the small boxes along the dimensions of the carton so that you can fill the carton with no wasted space. Since one edge of the small box is 7 inches, that edge of the small boxes should be placed along the side of the carton that is 42 inches long, since 42 is the only dimension that can be divided by 7 evenly. Thus you can put six small boxes along that side, but if you do that 6*6 soap boxes will have width 36 which would be greater than 25 & will exceed the carton width. so how can we just divide the volume of the carton & the soap's volume.

Or am I thinking too much :( ??
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Re: Soap boxes in a carton [#permalink] New post 03 Apr 2013, 08:20
I guess you are thinking too muck :)
For example you say:
"Since one edge of the small box is 7 inches, that edge of the small boxes should be placed along the side of the carton that is 42 inches long, since 42 is the only dimension that can be divided by 7 evenly."
Are you sure? I mean, what you say isn't wrong, but is not correct either (if we want to answer this particular question). On a side of 42 you can place 6 soaps on their "7-side"(6*7=42) or 2 soaps on their "6-side" and 6 soaps on their "5 side"(6*2+6*5=42). You can also rotate those soaps...
The correct approach is also the simplest in this case.

Hope it's clear
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink] New post 16 Apr 2013, 08:24
The answer works in this case... what if the dimension of the soap box was 6 7 8... This approach would fail then?
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink] New post 16 Apr 2013, 08:50
I'm not convinced... need some experts to help here....

I think the final answer should also include some sort of surface area calculations as well.

Hear my logic out

you have a box which is 42 60 25.. The best way to fit the soap box is 7 6 8

So you are going to have an array of 42/7=6 by 60/6=10 = 60 boxes

Now in 25 8 can only go 3 times

So total no of boxes that can be filled is 60x3=180
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Re: A grocer is storing soap boxes in cartons that measure 25   [#permalink] 16 Apr 2013, 08:50
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