Can a certain rectangular sheet of glass be positioned on

[jjjinapinch]

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

[Jay@ManhattanReview]

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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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

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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.

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.

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 does 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.

Answer: E