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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 [#permalink] New post 06 Sep 2004, 17:58
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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, 03:21, edited 1 time in total.
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 [#permalink] New post 06 Sep 2004, 18:32
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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] New post 06 Sep 2004, 18:43
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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 [#permalink] New post 06 Sep 2004, 18:44
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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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 [#permalink] New post 06 Sep 2004, 23:01
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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 can’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] New post 15 Mar 2012, 01:53
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] New post 15 Mar 2012, 03:59
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Antmavel wrote:
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


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] New post 12 Sep 2013, 01:31
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Re: A certain cube floating in a bucket of water has between 80 [#permalink] New post 12 Sep 2013, 01:54
Antmavel wrote:
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


1. 80% below water implies 20 % above water. 85% below water implies 15% above water
2. It is also given between 12 and 16 cu.cm above water.
3. So we can equate 20% to 16 cu.cm or 15% to 12 cu.cm. In either case 100% volume is 80 cu.cm
4. So length is cube root of 80 .

Choice A is the closest.
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Re: A certain cube floating in a bucket of water has between 80 [#permalink] New post 08 Nov 2013, 19:24
Bunuel, how did you find value of cube root 10. How is it possible to compute such a value under exam conditions.
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Re: A certain cube floating in a bucket of water has between 80 [#permalink] New post 08 Nov 2013, 22:38
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madn800 wrote:
Bunuel, how did you find value of cube root 10. How is it possible to compute such a value under exam conditions.


Hi,

Let us say you want to find out the cube root of 10. The cube of which number is immediately below 10? It is 2 because 2^3=8. Or you can see the cube of which number is immediately above 10? It is 3 because 3^3=27. So the cube root of 10 is between 2 and 3. You can further make it finer by seeing whether it is closer to 2^3 or 3^3.
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Re: A certain cube floating in a bucket of water has between 80 [#permalink] New post 07 Feb 2014, 01:27
Volume of cube of side s is s^3.

80% under water is 20% above water this implies

\frac{20}{100}*s^3 = 16

s^3=80

85% under water is 15% above water this implies

\frac{15}{100}*s^3 = 12

s^3 = 80

Now going to the answers if s=4 s^3 = 64. closer to 80 a possible answer.
if s=5 s^3 = 125. too far from 80. hence A is answer.
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Re: A certain cube floating in a bucket of water has between 80 [#permalink] New post 21 May 2014, 10:26
80 % below the surface means 20 % above the surface
85 % below the surface means 15% above the surface

If volume is V then 20% of V = 16 cubic meter => V = 80 cubic cm

or ,
If Volume is V then 15% of V = 12 cubic meter => =V = 80 cubic cm

Side of cube = cubic root (80)

we have 4^3 = 64 and 5^3 = 125
64 < 80 <125
4 < side <5
as 80 is nearer to 64 than to 125

hence side is approx 4 , Answer is A
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Re: volume [#permalink] New post 22 May 2014, 22:22
iwillcrackgmat wrote:
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 A is the best answer



Correcting.. A is the answer
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Re: volume   [#permalink] 22 May 2014, 22:22
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