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
