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DS from gmat club

by bblast » Sun Jan 09, 2011 8:21 am
A rectangular solid box is x inches long, y inches wide and z inches tall, where x , y , and z are positive integers, exactly two of which are equal. What is the total surface area of the box?

1. One face of the box has an area of 9 square inches.
2. One face of the box has an area of 81 square inches.

OA E
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Source: — Data Sufficiency |
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by anshumishra » Sun Jan 09, 2011 8:33 am
bblast wrote:A rectangular solid box is x inches long, y inches wide and z inches tall, where x , y , and z are positive integers, exactly two of which are equal. What is the total surface area of the box?

1. One face of the box has an area of 9 square inches.
2. One face of the box has an area of 81 square inches.

OA E
Total surface area = 2(xy+yz+zx) = ?

Statement 1:
xy = 9 -> Insufficient

Statement 2:
yz = 81 -> Insufficient

Combining 1 and 2 :
xy = 9
yz = 81
Only thing we need to find is zx = ?
yz/xy = 81/9 = 9
=> z = 9x
zx = 9x^2

Still we can't conclusively determine the sides or the expression 2(xy+yz+zx)

Hence, E

Also, using Plugging in numbers :
x= 1, y = 9, z = 9
x=3, y = 3, z = 27

xz has different values for these two pairs.
Thanks
Anshu

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