A noncompressible ball in the shape of a sphere is to be passed throug

#1
4/3 * pi * r^3
r=3

but we do not whether fitting of square is same/large/small to size of square
insuffcient
#2The square opening is the smallest square opening through which the ball will fit
okay we know now that vol of sphere = square area
from 1 &2
4/3 * pi * r^3 =s^2
r=2
we get s and 4s can be determined IMO C

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:

GMAT assassins aren't born, they're made,
Rich

https://e-gmat.com/blogs/a-noncompressi ... -solution/

chetan2u Bunuel EMPOWERgmatRichC

Hope you guys are doing well

How can the diameter of the sphere be equal to the side of the square as it is clearly mentioned that the ball has to be passed through?? To be passed through the square, shouldn’t the side of the square be slightly greater than the diameter of the sphere/ball? It cannot be equal to the diameter of the sphere, if so then wouldn’t the ball get stuck at the top of the square?

Is the answer C because logically there will be one and only one minimum number closest to 4, whatever the number may be?

Looking forward to hearing from you guys?

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Yes, you are correct. The smallest means it would be just close to the diameter of sphere. Even a fraction of 1 mm will ensure free passage.

Logically, yes exact size of dia of sphere may restrict the passage, but, then 4.00001 would allow the passage, and there can be only one that is THE SMALLEST.

Understood

Thank you for your response, truly appreciate it ?

C
Statement 2 ---> gives the condition that makes 2r(diameter of sphere) = a (side of a square). Insufficient, as no absolute value can be found
Statement 1 ---> some random values. Since we dont the exact area of square opening, it can be any arbitary value. Insufficient

On combining , C seems to be the OA.

(1) \(\frac{4}{3}πr^3=\frac{4}{3}π2^3\), But don't know about the size of the opening. Insufficient.

(2) We don't have information about the radius r of the opening. Insufficient.

Considering both:
We have all the information. Sufficient.

The answer is C

Hi Bunuel,

I dont see ny value common value in both statement, how come ans is C
Plaesehelp me to understand

What common value are you looking for? The question basically asks for the perimeter of a square in which a circle of radius of 2 is inscribed. The radius of 2 means that the side of the square is 4, and the perimeter is 16.

Answer: Option C

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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

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