A certain cube floating in a bucket of water has between 80

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A certain cube floating in a bucket of water has between 80 [#permalink]

06 Sep 2004, 18:58

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A certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water. If between 12 and 16 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately

A. 4
B. 5
C. 7
D. 8
E. 9

[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Mar 2012, 04:21, edited 1 time in total.

Edited the question

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06 Sep 2004, 19:32

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Backsolving,

If sides are 7, vol=7^3=343
80%= 274.4, 85%=291.55
so vol above water, between 68.6 and 51.45 -->too big

If side are 4, vol = 64
80%=51.2, 85%=54.4
vol above water between 12.8 and 9.6

So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
80%= 100, .85%=106.25
vol above water bwtween 18.75-25

(Sides are 4 cubic centimeters)

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Re: volume [#permalink]

06 Sep 2004, 19:43

if L be the side
using data1
L^2*0.2*L=12 or L=60^1/3 = 4 appx
using data2
L^2*0.15*L=16 or L=106^1/3 = 4+ appx (but less than 5)

Hence A is safest bet!

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06 Sep 2004, 19:44

Quicker way:

If 80% underwater => 16 cc above water:

Thus, 0.2V = 16, or V = 80 cc. Cube root of 80 is 4.31, which is the length of each side.

If 85% underwater => 12 cc above water:

Thus, 0.15V = 12, or V = 80 cc, and the answer is the same: 4.31 --> aprroximated to 4.

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07 Sep 2004, 00:01

Best way to approach this problem is to plug in the answers since the
answers give us the side of the cube.

If we start with the middle choice, C, then we have a cube with
side 7. If the cube has a side of 7 then it will have a volume of 343. We are told that between 80 and 85% of the volume is below the surface of the water, which means that between 15 and 20% of the volume is above the surface.

If the volume of the cube is 343 then 20% is about 68 and 15% is about
51. Neither of these numbers is between the 12 and 16 cubic centimeters that are supposed to be above water, so clearly this canâ€™t be the answer.

Since the numbers are too large with need to trysomething smaller. Pick one of the smaller choices and try again. Then you'll find it :wink:

I can see by the number of good answers to my several daily problems that everybody is sharp and ready for the GMAT

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Re: volume [#permalink]

15 Mar 2012, 02:53

let side = a
80% underwater => 16 cc

Therefore , 20%(V) = 16, or a^3 = 80 cc. => a = 4.31,

If 85% underwater => 12 cc above water:

Thus, 15%(V) = 12, or a^3 = 80 cc, a = 4.31

So C is the best answer
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Re: A certain cube floating in a bucket of water has between 80 [#permalink]

15 Mar 2012, 04:59

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Antmavel wrote:

Since between 80 and 85 percent of the cube's volume is below the surface of the water and between 12 and 16 cubic centimeters of the cube's volume is above the surface of the water, then 85-80=5% or 16-12=4 cubic centimeters of the volume is sometimes below and sometimes above the surface of the water. V*5%=4 cubic centimeters --> V=80 --> side=\sqrt[3]{80}=2\sqrt[3]{10}\approx{4.2}.

Answer: A.
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Re: A certain cube floating in a bucket of water has between 80 [#permalink] 15 Mar 2012, 04:59

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A certain cube floating in a bucket of water has between 80

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A certain cube floating in a bucket of water has between 80

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