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12 Aug 2020, 02:48
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C
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Difficulty:
15%
(low)
Question Stats:
88% (01:50) correct
12%
(02:42)
wrong
based on 51
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Not Attempted Yet
What is the maximum number of rectangular boxes, each measuring 2 inches by 3 inches by 5 inches, that can be packed into a rectangular packing box measuring 18 inches by 19 inches by 35 inches, if all of the smaller boxes are aligned in the same direction?
(A) 296
(B) 356
(C) 378
(D) 412
(E) 424
(A) 296
(B) 356
(C) 378
(D) 412
(E) 424
yashikaaggarwal
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12 Aug 2020, 05:44
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The maximum no. of box that can be aligned in box in any way = Total volume of large box/ volume of small box
=> 19*18*35/ 2*3*5 = 399
we can eliminate options D and E
If the boxes has to be aligned in same direction, it has to follow the constraint of layers in big boxes.
there can be 7 layers of 5 inch in 35 inch height of box
therefore if there are x boxes per layer.
there will be 7x boxes in all layers.
only C among all is a multiple of 7.
Answer is C
=> 19*18*35/ 2*3*5 = 399
we can eliminate options D and E
If the boxes has to be aligned in same direction, it has to follow the constraint of layers in big boxes.
there can be 7 layers of 5 inch in 35 inch height of box
therefore if there are x boxes per layer.
there will be 7x boxes in all layers.
only C among all is a multiple of 7.
Answer is C
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12 Aug 2020, 06:41
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SajjadAhmad
We can count the number of boxes that will fit in the height, length, and width with a certain arrangement and quickly calculate our options.
For example, let the 2-inch side fill the 18-inch width, let the 3-inch side fill the 19-inch length. Finally, the 5-inch side will fill the 35-inch height.
With this arrangement we have 18/2 = 9 boxes wide, 19/3 => 6 boxes long, and 35//5 = 7 boxes high. This arrangement results in 9*6*7 = 54*7 = 350+28 = 378 boxes total.
There are other arrangements but our goal is to stack the maximum numbers, we can see the 5-inch side slots perfectly into the 35-inch side and that should be kept. The only other possible arrangement is letting the 2-inch side fill the 19-inch length and the 3-inch side fill the 18-inch width, resulting in 19/2 => 9 and 18/3 =6, which are the same numbers.
Ans: C
