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Identical cylinders

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by manik11 » Wed May 25, 2016 8:16 am
If the maximum number of identical cylinders, standing upright and touching the edges, that can be fit into a rectangular box with a square base is 200, what is the volume of the box?

(1) The radius of each cylinder is 5 centimeters.
(2) The height of the box is 80 centimeters.

OA : E
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Source: — Data Sufficiency |

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by [email protected] » Wed May 25, 2016 9:38 am
Hi manik11,

This question can be solved with a bit of logic and understanding the type of information that you would NEED to know to answer the given question. Based on the information in the prompt, we know that a box has a square base and that 200 identical cylinders could fit in the box (if the cylinders were touching the edges of the box). We're asked for the VOLUME of the box. By definition, we'll need actual numbers for the base and the height of the box, to answer this question.

(1) The radius of each cylinder is 5 centimeters.

This tells us nothing about the height of the cylinders, the base of the box nor the height of the box. Changing the height of the cylinders and/or the base or height of the box will change the volume of the box.
Fact 1 is INSUFFICIENT

(2) The height of the box is 80 centimeters.

This tells us nothing about the base of the box nor anything about the dimensions of the cylinders. Different-sized cylinders and/or a different-sized base will change the volume of the box.
Fact 2 is INSUFFICIENT

Combined, we don't know the height of the cylinders nor the base of the box. Changing those variables will change the volume of the box.
Combined, INSUFFICIENT.

Final Answer: E

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by OptimusPrep » Thu May 26, 2016 7:05 pm
manik11 wrote:If the maximum number of identical cylinders, standing upright and touching the edges, that can be fit into a rectangular box with a square base is 200, what is the volume of the box?

(1) The radius of each cylinder is 5 centimeters.
(2) The height of the box is 80 centimeters.

OA : E
The question simply asks us to know the volume of the box. Hence we need to know the l, b and h of the box.

Statement 1: radius or cylinder = 5.
We know the radius, but do not know the height of each cylinder.
Hence we do not know the height of the box.
INSUFFICIENT

Statement 2: height of the box = 80
We do not know the length and the base.
INSUFFICIENT

Combining both statements:
Still we do not know the height of the box and the base of the box.
Still INSUFFICIENT

Correct Option: E
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by nchaswal » Sat May 28, 2016 6:04 am
OptimusPrep wrote:
manik11 wrote:If the maximum number of identical cylinders, standing upright and touching the edges, that can be fit into a rectangular box with a square base is 200, what is the volume of the box?

(1) The radius of each cylinder is 5 centimeters.
(2) The height of the box is 80 centimeters.

.
.
.
.
.
Still we do not know the height of the box and the base of the box.
Still INSUFFICIENT

Correct Option: E

Dear OptimusPrep

Are you sure we need to know both L & B of the box? it is clearly given that L & B are the same as the base is square.

This question could have been solved easily if one more input was given: That Cylinders are not kept on top of one another. That way the BASE area as well as height of the box will easily be known and hence the volume of the box.
It is GMAT. So what?
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