Data Sufficiency

AbeNeedsAnswers wrote:A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening?

(1) The radius of the ball is equal to 2 inches.
(2) The square opening is the smallest square opening through which the ball will fit.

C

Source: Official Guide 2020

Let's take each statement one by one.

(1) The radius of the ball is equal to 2 inches.

Certainly insufficient. The square of any dimension: sufficient enough to let the ball pass to very large.

(2) The square opening is the smallest square opening through which the ball will fit.

Certainly insufficient.

(1) and (2) together

=> Side of the square = Diameter of the ball = 2*2 = 4 inches

=> Perimeter of the square = 4*4 = 16 inches. Sufficient.
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Hi All,

We're told that a non-compressible ball in the shape of a SPHERE is to be passed through a SQUARE opening in a board. We're asked for the perimeter of the opening. While this question might seem a bit quirky, it's actually based on some basic Geometry rules. To start, it's worth noting that the 'widest' part of a sphere is the DIAMETER, so for the sphere to fit through a square hole, we will have to compare the diameter to the side length of the square.

(1) The radius of the ball is equal to 2 inches.

With Fact 1, we know that the diameter of the sphere is 4 inches, but we don't know anything about the square hole.
Fact 1 is INSUFFICIENT

(2) The square opening is the smallest square opening through which the ball will fit.

With Fact 2, we know that the sphere WILL fit through the hole, but we still don't know the exact perimeter of the square.
Fact 2 is INSUFFICIENT

Combined, we know...
-The radius of the ball is equal to 2 inches.
-The square opening is the smallest square opening through which the ball will fit.

We know that the square opening is as small as possible, but would still have to accommodate the diameter of 4. Thus, we have a 4x4 square and the answer to the question is 16.
Combined, SUFFICIENT

Final Answer: C

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