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Can a certain rectangular sheet of glass be positioned on

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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Can a certain rectangular sheet of glass be positioned on

Post Thu Aug 03, 2017 12:16 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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.

    Official Guide question
    Answer: E

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    Post Thu Aug 03, 2017 8:58 pm
    jjjinapinch 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.

    Official Guide question
    Answer: E
    The rectangular sheet of glass can cover the rectangular tabletop so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop if

    1. The longer side of the rectangular sheet of glass ≥ The longer side of the rectangular tabletop
    2. The shorter side of the rectangular sheet of glass ≥ The shorter side of the rectangular tabletop

    Statement 1: The tabletop is 36 inches wide by 60 inches long.

    We do not have the dimensions of the rectangular sheet of glass. Insufficient!

    Statement 2: The area of one side of the sheet of glass is 2,400 square inches.

    Neither do we have the dimensions of the rectangular sheet of glass nor do we have the dimensions of the rectangular tabletop. Insufficient!

    Statement 1 & 2:

    From (1), we have the dimensions of the rectangular tabletop, but from (2), we do not have the dimensions of the rectangular sheet of glass.

    Merely by knowing the area of the sheet of glass is insufficient.

    Let's take two extreme cases.

    Case 1: Given the area of the sheet of glass = 2400 sq inches, say the shorter side of the sheet = 1 inch, thus the longer side = 2400/1 = 2400 inches

    The tabletop cannot be covered! The answer is NO.

    Case 2: Given the area of the sheet of glass = 2400 sq inches, say the shorter side of the sheet = 40 inches, thus the longer side = 2400/40 = 60 inches

    1. The longer side of the rectangular sheet of glass (60) = The longer side of the rectangular tabletop (60)
    2. The shorter side of the rectangular sheet of glass (40) > The shorter side of the rectangular tabletop (36).

    The tabletop can be covered! The answer is Yes.

    No unique answer. Insufficient.

    The correct answer: E

    Hope this helps!

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    Post Sat Aug 26, 2017 10:46 am
    Hi jjjinapinch,

    We're asked if a certain rectangular sheet of glass can be positioned on a rectangular tabletop so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop. This is a YES/NO question. To answer it, we'll need specific information about the size of the sheet and the size of the tabletop.

    1) The tabletop is 36 inches wide by 60 inches long.

    Fact 1 gives us the dimensions of the tabletop, but we don't know anything about the dimensions of the sheet.
    Fact 1 is INSUFFICIENT

    2) The area of one side of the sheet of glass is 2,400 square inches.

    Fact 2 gives us the AREA of the sheet, but NOT its specific dimensions - and we don't know the dimensions of the table. The dimensions of the sheet could be a variety of different combinations, including....
    40 inches by 60 inches
    30 inches by 80 inches
    1 inch by 2400 inches
    Etc.
    Fact 2 is INSUFFICIENT

    Combined, we know:
    The tabletop is 36 inches by 60 inches.
    The AREA of the sheet is 2400 square inches.
    IF.... the dimensions of the sheet are:
    40 inches by 60 inches... then the answer to the question would be YES.
    30 inches by 80 inches... then the answer to the question would be NO.
    Combined, INSUFFICIENT.

    Final Answer: E

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