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Interesting GMATFix Problem-8

by arora007 » Tue Sep 21, 2010 12:51 pm
What is the largest possible volume of a rectangular box placed inside cylinder C?
1) C has a height of 1 foot
2) C has a volume of x cubic feet
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Source: — Data Sufficiency |
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by kvcpk » Wed Sep 22, 2010 6:32 am
arora007 wrote:What is the largest possible volume of a rectangular box placed inside cylinder C?
1) C has a height of 1 foot
2) C has a volume of x cubic feet
1) C has a height of 1 foot
Box can span across length and breadth too.
Assume a big oil well of 1 foot height. Rectangular box can be very big.
Assume a small cap of 1 foot height. Rectangular box can be small.
So INSUFF

2) C has a volume of x cubic feet
pi* r^2 * h = x
Qn i sasking for a specific value. We do not have any specifics in this stmt. INSUFF

Combining:
pi* r^2 * h = x
pi* r^2 = x
Still the same problem. If we knew what r or x is, we would have had a fair chance to calculate.
but here we dont have. Hence INSUFF

pick E.
Last edited by kvcpk on Wed Sep 22, 2010 7:32 pm, edited 1 time in total.
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by arora007 » Wed Sep 22, 2010 2:05 pm
try again...wrong choice!
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by sanabk » Wed Sep 22, 2010 2:13 pm
The largest possible volume of a rectangular box is when it is a Cube.
1) C has a height of 1 foot
Volume of Cube=1 cubic feet
- SUFF

2) C has a volume of x cubic feet
Pi*r^2*h=x cubic feet
-Not SUFF

Answer: A
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by arora007 » Wed Sep 22, 2010 2:16 pm
OA is B
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by garudcvg » Wed Sep 22, 2010 2:41 pm
The largest square that can fit in a circle is one that has sides equal to SQRT(2)r. This can be derived when a square is inscribed within a circle. Draw a circle then draw its diameters, then connect the four corners for a diameter to get this largest square. You can then run Pythagorean equation to determine the side of the square since you know the radius of the circle. This will give you the value of SQRT(2)r, where r is the radius of the circle.

The volume of the rectangular box will the area of this square times the height of the cylinder

Area of Square = Side X Side = 2rr ----- Equation 1
Volume of cylinder = Pi X rr X h = x------Equation 2
Volume of Rectangular Box = Area of Square X Height of Cylinder = 2rr X h -------Equation 3

rr X h = x/Pi .Substitute this value in equation 3 to get the volume of the cylinder. Hence Answer choice is B. This information is sufficient to largest possible volume of the rectangular box.

Hope it helps...it is kinda twisted.
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