Will at least three identical cubes fit inside a cylindrical shipping container? (1) The edge of one of the cubical box

[BTGmoderatorDC]

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

[Jay@ManhattanReview]

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
_________________
Manhattan Review

Locations: Manhattan Review Jayanagar | GMAT Prep Tarnaka | GRE Prep Madhapur | Kukatpally GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

[swerve]

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

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

Let the diameter of cylinder \(= 5\)
\(\Longrightarrow\) Edge of cube \(= \dfrac{4}{5} \cdot 5 = 4\)

For the cube to fit in the cylinder, the diagonal of the cube should be at least equal to the diameter
\(\Longrightarrow\) Diagonal \(= 2\sqrt{2}\cdot\)edge
\(\Longrightarrow\) Diagonal \(= 42\sqrt{2} \approx 5.65 \)

So, the cube will definitely not fit in the cylinder - A Definite NO

Sufficient \(\Large{\color{green}\checkmark}\)

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

Nothing can be deduced about the radius and height of the cylinder with the given volume.

Insufficient \(\Large{\color{red}\chi}\)

The correct option is _A_