Problem Solving

Hi M7MBA,

We're told that a grocer is storing soapboxes in cartons that measure 25 inches by 42 inches by 60 inches and the measurement of each soapbox is 7 inches by 6 inches by 5 inches. We're asked for the MAXIMUM number of soapboxes that can be placed in each carton. To maximize the number of boxes that we can put in this carton, we have to use as much of (if not all of) the space in the carton. Thus, we have to "orient" the boxes in such a way that we use up all of the space in the carton.

The carton's dimensions are 25 x 42 x 60 and each box has dimensions of 5 x 6 x 7

To maximize the number of boxes, I'm going to "line up" the 5 with the 25 and the 7 with the 42.

25/5 = 5 and 42/7 = 6, so the "bottom layer" of boxes will be 30 boxes.

Now the 6 will "line up" with the 60.... 60/6 = 10, so we'll have 10 layers of 30 boxes...and all of carton will be completely full.

(10)(30) = 300 boxes.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

M7MBA wrote:A grocer is storing soapboxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soapbox is 7 inches by 6 inches by 5 inches, then what is the maximum number of soapboxes that can be placed in each carton?

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

[spoiler]OA=D[/spoiler]

Source: Princeton Review

First, we must make sure that soap boxes can be placed in a carton without any empty space between the soap boxes. Since 25 is a multiple of 5, 60 is a multiple of 6 and 42 is a multiple of 7; it is possible to position the soap boxes in the carton without any empty space.

Now that we know the soap boxes can be placed without any space, we can simply divide the volume of a carton by the volume of a soap box to find the maximum number of soap boxes that can be contained in a carton. The maximum number of soap boxes that can be placed in each carton is:

(25 x 42 x 60)/(7 x 6 x 5) = 5 x 6 x 10 = 300

Answer: D