Bunuel wrote:
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?
A. 0
B. 36
C. 180
D. 216
E. 384
Are You Up For the Challenge: 700 Level QuestionsThe rectangular box is 10 x 12 x 16. For the side length of 10: We can occupy two lengths of 4's. Subtract the two four's and 2 is left.
For the side length of 12: We can occupy the entire area with three 4's.
For the side length of 16: We can occupy the entire area with four 4's.
Imagine the length of 10 as the height, when we fill this box up, we have the entire base of 12 * 16 filled with a height 2 missing. Therefore after filling up the rectangular box, we will just be left with a volume 2 * 12 * 16 left, 2 * 12 * 16 = 384.
(Note this doesn't translate over when two sides are not fully covered, we simply subtract volumes at that point).
Ans: E
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to
guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the
fastest in the world. Feel free to
reach out!