Question

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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (E)

Statements (1) and (2) together are not sufficient.

1. The length and width of the tabletop are given, but nothing can be determined about the dimensions of the sheet of glass; Thus, statement 1 is insufficient.
   
2. The area of the sheet of glass is given, but nothing can be determined about the dimensions of the tabletop. Thus, statement 2 is insufficient.
   
3. (1) and (2) together are not sufficient because the information given does not specify the length and width of the sheet of glass. For example, the length and width of the sheet of glass could be $40$ inches and $60$ inches and, since $40\ge 36$ and $60\ge 60$, the answer to the question would be positive. On the other hand, the length and width of the sheet of glass could be $100$ inches and $24$ inches, and in this case the answer to the question would be negative because $24$ is not greater than or equal to $36$ or $60$.