Can more than thirteen balls of radius R be fitted (without compressin

Question

Can more than thirteen balls of radius R be fitted (without compressing) inside a rectangular box?

(1) The internal dimensions of the rectangular box are 2R, 3R, and 9R
(2) The volume of the rectangular box is 54R^3

sayyamdeshpande · Answer

The answer should be D, first statement tells us that volume of box is 54R^3 and volume of ball is 4 pi R^3/3. dividing them gives A sufficient.
Statement 2 gives us the same thing as we got in statement 1
hence, D not A

suchita2409 · Answer

Statement 2 for sure says the volume but we donot know the dimensions.
Until and unless we donot know the dimensions we cannot say the no. of balls fitted .

Statement 1 gives us dimension.We can find volume.And hence the number of balls.

A it is!

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IanStewart · Answer

What is the source? The answer is D, not A.

Statement 1 tells us the dimensions of the box, at least relative to the dimensions of the spheres, so we can answer the question - there's technically no reason to do that, because it's not a PS problem, but it's a bit useful in this particular question. Notice we can only fit at most 4 spheres in this box, since the diameter of a sphere is 2R. That's also the width of the box, so the spheres will need to touch either side of the box. The height is only 3R, so you can't stack spheres on top of each other (the diameter of the spheres is too big). All you can do is arrange the spheres in a row, and the length of the box is only 9R, so you can only fit four spheres in a row if their diameter is 2R. So Statement 1 is sufficient to give us a 'no' answer.

Statement 2 is also sufficient - the volume of 14 spheres of radius R is bigger than 54R^3, so there's no chance they'll fit in the box no matter what dimensions it has.

You don't need to know volume formulas for spheres for the GMAT though.

vatsalkap · Answer

So if we are comparing volume in statement 2, why didn't we do the same for statement 1?

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Lipun · Answer

I guess statement 2 was supposed to be a trap because statement 1 is sufficient to answer. To serve as a trap, the volume of the box had to be more than the volume of 13 balls. Since we still would not have any idea about the dimensions, it would have been insufficient.

But as you rightly pointed out, the statement by itself becomes sufficient because of the value presented.

Regards
Lipun

Can more than thirteen balls of radius R be fitted (without compressin

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Can more than thirteen balls of radius R be fitted (without compressin

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