Can a certain rectangular sheet of glass be positioned on a

SOLUTION

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.

Even when we consider the two statements together we can have for instance the following cases: if the dimensions of the glass are 40*60, then the answer would be YES but if the dimensions of the glass are 1*2,400, then the answer would be NO. Not sufficient.

Answer: E.
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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.

Question can be restated as "Is Glass sheet rectangular & of same dimensions as that of tabletop?"
1) No info is given about glass sheet dimensions- Insufficient
2) No info is given regarding the dimensions of tabletop & its not stated whether the glass sheet is Rectangular, Square or Parallelogram etc.--->Insufficient
1+2) No info is given whether the glass sheet is Rectangular, Square or Parallelogram etc ---Insufficient

Answer E

The question says "Can a certain rectangular sheet of glass..."

Maybe it looks strange the information in statement (2): "The area of one side of the sheet of glass..."
But, the sheet of glass is in fact a 3D object, a rectangular box, probably quite thin. So, we are talking about a rectangular side with the largest area. I don't think they cut the glass at an angle other than 90 degrees.
Anyway, the answer is E because the area of 2,400 although greater than 36*60 = 2,160, if the dimensions of the sheet are 30 and 80, it will not cover the tabletop.
But if the dimensions are 40 and 60, then yes.
The sheet of glass needs to cover the tabletop, not necessarily to be of identical dimensions. In other words, the sheet of glass can be larger than the tabletop, although this isn't practical....
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Already mentioned in the question " Rectangular glass sheet"

One part of the question I understood " that it covers entire table-top" , to suffice this condition glass sheet must have as same dimensions (length and breadth) as table.
What does " its edges are parallel to the edges of the tabletop" mean ?

It means that it must be as shown on the first figure not, for example, as on the second:
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Hi soh_acca,

You posted this question in some other forum also, so copying my response.
Also, as a general rule, search a question on GMAT Club before posting it again.

Statement 1 is not sufficient because we do not have any information about the sheet
Statement 2 is not sufficient because we do not have any information about the table top

Combining the both, we do not have any information about the orientation of the sheet.

Hence both statements combined can also not answer the question

Hence option E

As you read the question, you should first think what are the variables that is required to perfectly tell whether the glass sheet covers the table top or not. So, we have to know the table size as well as the glass sheet size.
(1) gives us the table size only. {Insufficient}
(2) gives us the area of the glass sheet only. {Insufficient}

When we combine both of them, we are not sure if the glass sheet is a rectangle or a square or circular or any other polygon. According to statement (1), the table's size is 36*60=2,160 sq.in. which is smaller than the area of the glass sheet i.e. 2,400 sq in. If the area of the table would have been more than 2400, then we could have selected 'C' as the right answer, but in this case it is not so. Hence, E.

{Kudos will be appreciated ) }

Dear soh_acca,
It appears that the Jedi Master skywalker18 already gave you a good answer, but I will respond also. I like the fact that the dimensions of the table in this problem are a few hundredths away from the Golden Ratio.

(1) Tell us about the exact dimensions of the table and absolutely nothing about the piece of glass. Insufficient.

(2) Now, we know the total area of the glass, although not the exact dimensions, and we know zilch about the size of the table.

(1) & (2) now, we know about the exact dimensions of the table and the area, but not the exact dimension, of the glass. Here's a picture with the table (in green) and a few different pieces of glass (in purple).

As you can see, if the glass is 40 x 60, it will neatly cover the entire table top, but if it is 24 x 100, there is no way to position it so that it covers the entire table at once (unless we strategically break the glass into rectangles, which is outside the scope of this question).

When all you know is the area of a rectangle, you have no idea of the "shape" of the rectangle, the relative sizes of the length vs. the width. That's very important to appreciate.

Does all this make sense?
Mike
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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 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.

The answer is E.
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Hi All,

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:

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

Bunuel
I have a doubt here: If we take 30*80 , it will not cover the entire tabletop .
if we take 60*40 , it will cover the entire top but it's edges won't be parallel to that of tabletop
Hence the answer should be C instead of E .

Please correct me if I missed any point.

For 30*80, case the answer to the question is NO.
For 40*60, case the answer to the question is YES.

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

P.S. When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.
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For 40*60 the answer to the question should be NO as it won't be parallel to that of tabletop
It will cover the tabletop but it won't be parallel so shouldn't it be NO?

Two sides of the glass will coincide the two sides of the tabletop, but we can consider this to be parallel.

Else you can consider other dimensions of the glass, for example, 2400/61 =~39,... by 61.
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Dear All,

My question is why are we skipping over the part "Glass sheet edges Parallel to the edges of the table top''?????

Its clear from (1) and (2) that no matter of what combination of edge dimensions for 2400 square inches (60,40)
or (100,24) etc, it will never be (36,60) and hence the edges of Glass Sheet will NEVER be parallel to the edges of the Table top, and hence the Answer would be 'C' since we can clearly state that from (1) and (2) we can never get a the edges parallel.

Kindly advise

Hi RB95,

I think that you may have misinterpreted the meaning of the information that this prompt gives us to work with. As an example, draw two parallel lines... Did you draw the second line exactly "on top" of the first line? You probably did not - because that is NOT what "parallel" means. We're asked if the glass sheet covers the entire table-top AND the edges of the sheet are parallel with the edges of the table. That is NOT the same as asking "does the glass sheet have the same dimensions as the table-top."

You might consider a 3x3 glass sheet and a 2x2 table-top. The sheet would cover the entire table-top and you could arrange the sheet so that the 4 edges of the sheet were parallel to the 4 edges of the table-top (each edge of the sheet would just be 1/2 an inch away from each edge of the table).

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

Hi Bunuel,

My question is what if the second statement provided information about the exact dimensions of the rectangular sheet of glass say “one side of the sheet of glass is 24 inches wide and 55 inches long”. Would the answer be C then? I feel it would still be E since we still don’t know whether the edges of the glass are parallel to the edges of the tabletop and none of the statements provide information about that.
Or is it that the rectangular piece of glass automatically means that the vertical edges are going to be 90 degrees and thus parallel to the tabletop? And hence the answer would be C.

Thanks,
Udit

The answer would be C. We'd be able to give a NO answer to the question. 24*55 sheet of glass cannot cover the entire tabletop which is 36*60.

C would be the answer too, if (2) were: The sheet of glass is 40 inches wide by 60 inches long. In this case, we COULD position the sheet of glass, so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop. So, the answer to the question would be YES, we CAN position the sheet of glass, so that it covers the entire tabletop and its edges are parallel to the edges of the tabletop
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Thanks Bunuel,
I understand your logic about the glass covering the table.
However, my doubt is related to whether the edges of the glass are parallel to the edges of the tabletop portion of the question stem. Since it is a rectangular sheet of glass, do we have to assume that all its verticle edges would be 90 degrees? Meaning a rectangular box or a rectangular sheet would by default have their edges parallel to a rectangular tabletop?

Thanks,
Udit