swerve 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.

The OA is C

Source: Official Guide

Let's take each statement one by one.

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

No information about the side of the board. Insufficient.

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

Certainly insufficient.

(1) and (2) together

The minimum length of the side of the square board would be 2*radius. Thus perimeter of the opening = 4*2*radius = 4*2*2 = 16 inches. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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swerve wrote: ↑

Sun Dec 29, 2019 11:19 am

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.

The OA is C

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the perimeter of the square opening so that a noncompressible spherical ball can be passed through the opening. Notice that the opening must have a side length that is at least the diameter of the ball in order for the ball to pass through it.

Statement One Alone:

Since we know the radius of the ball is 2 inches, the diameter of the ball is 4 inches. Therefore, if the square opening has a side length of at least 4 inches, then the ball will pass through it. However, since the side length of the opening can be any value greater than or equal to 4 inches, we can’t determine the perimeter of the opening. Statement one alone is not sufficient.

Statement Two Alone:

Without knowing how large the ball (e.g., the radius of the ball) is, we can’t determine the perimeter of the opening, despite the fact that the square opening is the smallest square opening through which the ball will fit. Statement two alone is not sufficient.

Statements One and Two Together:

We know the radius of the ball is 2 inches and the square opening is the smallest square opening through which the ball will fit. Thus, the square opening must have a side length of exactly 4 inches. Therefore, its perimeter is 16 inches. Both statements together are sufficient.

Answer: C

swerve wrote: ↑

Sun Dec 29, 2019 11:19 am

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.

The OA is C

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the perimeter of the square opening so that a noncompressible spherical ball can be passed through the opening. Notice that the opening must have a side length that is at least the diameter of the ball in order for the ball to pass through it.

Statement One Alone:

Since we know the radius of the ball is 2 inches, the diameter of the ball is 4 inches. Therefore, if the square opening has a side length of at least 4 inches, then the ball will pass through it. However, since the side length of the opening can be any value greater than or equal to 4 inches, we can’t determine the perimeter of the opening. Statement one alone is not sufficient.

Statement Two Alone:

Without knowing how large the ball (e.g., the radius of the ball) is, we can’t determine the perimeter of the opening, despite the fact that the square opening is the smallest square opening through which the ball will fit. Statement two alone is not sufficient.

Statements One and Two Together:

We know the radius of the ball is 2 inches and the square opening is the smallest square opening through which the ball will fit. Thus, the square opening must have a side length of exactly 4 inches. Therefore, its perimeter is 16 inches. Both statements together are sufficient.

Answer: C