Hi All,
We're told that the length, width, and height of a rectangular box, in centimeters, are L, W, and H, respectively, the VOLUME of this box is V cubic centimeters and the TOTAL SURFACE AREA of the 6 sides of this box is A square centimeters. We're asked for the value of V/A. This question is based around some standard Geometry formulas for solids and can be solved by TESTing VALUES.
To start, Volume of a rectangular solid is V = (L)(W)(H) and Total Surface area is SA = 2(L)(W) + 2(L)(H) + 2(W)(H).
(1) At least 2 of L, W, and H are equal to 5.
Fact 1 tells us that 2 (or perhaps all 3) of the dimensions are equal to 5, but that still leads to a number of different answers to the question.
IF...
L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6.
L = 5, W = 5, H = 1, then the Volume = (5)(5)(1) = 25 and Total Surface Area = (2)(5)(5) + (2)(5)(1) + (2)(5)(1) = 70... so the answer to the question is 25/70 = 5/14.
Fact 1 is INSUFFICIENT
(2) L, W, and H all have the SAME value.
Fact 2 tells us that we're actually dealing with a CUBE, but the answer to the question will still vary depending on the side length.
IF....
L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6.
L = 1, W = 1, H = 1, then the Volume = (1)(1)(1) = 1 and Total Surface Area = (2)(1)(1) + (2)(1)(1) + (2)(1)(1) = 6... so the answer to the question is 1/6.
Fact 2 is INSUFFICIENT
Combined, we know...
At least 2 of L, W, and H are equal to 5.
L, W, and H all have the SAME value.
When combining the two Facts, it's clear that we're dealing with a cube with a side length of 5, so the answer to the question is 5/6.
Combined, SUFFICIENT
Final Answer:
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Rich
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