BTGmoderatorDC wrote: ↑

Thu Feb 13, 2020 5:00 pm

Will at least three identical cubes fit inside a cylindrical shipping container?

(1) The edge of one of the cubical boxes is 4/5 as wide as the diameter of the cylinder.

(2) If the cylinder had 50% more capacity, seven of the identical cubical boxes could fit inside the cylinder

OA A

Source: Princeton Review

Let's take each statement one by one.

(1) The edge of one of the cubical boxes is 4/5 as wide as the diameter of the cylinder.

The maximum length of the edge of the cube to be fitted inside a cylinder with d diameter = d/√2 = d/1.414.

Given is the length of the edge = 4/5 of d = d/(5/4) = d/1.25

Since d/1.25 > d/1.414, we can conclude that no cube can fit inside the cylinder. Sufficient.

(2) If the cylinder had 50% more capacity, seven of the identical cubical boxes could fit inside the cylinder.

We are not sure whether the capacity enhancement of the cylinder is taken place after increasing its (1) only diameter (2) only length (3) diameter as well as length, if yes in what proportion? (4) diameter increased, but length decreased (5) length increased, but diameter decreased

So there are many possibilities. So, we cannot conclude wether at least three identical cubes can fit. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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