Bunuel wrote:
Can a certain rectangular sheet of glass be positioned on a rectangular tabletop so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop?
(1) The tabletop is 36 inches wide by 60 inches long.
(2) The area of one side of the sheet of glass is 2,400 square inches.
We need to determine whether a rectangular sheet of glass can cover an entire rectangular tabletop. We are given that the edges must be parallel to the table top; however, we know neither the dimensions of the sheet of glass nor the dimensions of the tabletop.
Statement One Alone:The tabletop is 36 inches wide by 60 inches long.
Since we do not have any information about the dimensions of the rectangular sheet of glass, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:The area of one side of the sheet of glass is 2,400 square inches.
Since we do not have any information about the dimensions of the tabletop, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:Using the information from statements one and two we know the following:
1) The tabletop is 36 inches wide by 60 inches long.
2) The area of one side of the sheet of glass is 2,400 square inches.
While initially we may think we have enough information to solve the problem, we actually do not, because we do not know the exact dimensions of the sheet of glass.
With an area of 2,400 square inches, we can have different lengths and widths of the sheet of glass. Some of these lengths and widths will allow the sheet to cover the table, while others will not. Let’s consider two cases.
Case # 1
Width of glass = 24 inches
Length of glass = 100 inches
Width of table = 36 inches
Length of table = 60 inches
We see that the width of the glass is shorter than the width of the table, so in case #1, the sheet of glass d
oes not cover the entire table top.Case # 2
Width of glass = 40 inches
Length of glass = 60 inches
Width of table = 36 inches
Length of table = 60 inches
We see that the width of the glass is longer than the width of the table and the length of the glass is equal to the length of the table, so in case #2, the sheet of glass
does cover the entire table top.The answer is E.
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