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# A rectangular area is covered with a rectangular rug. If the

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Current Student
Joined: 11 May 2008
Posts: 552
A rectangular area is covered with a rectangular rug. If the [#permalink]

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25 Jul 2008, 18:13
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A rectangular area is covered with a rectangular rug. If the respective sides of two rectangles are parallel to each other and have a distance of 5cm, what is the area of the large rectangle?
(1) The length of the rug is twice as long as the width of the rug.
(2) The area of the rug is 18 square centimeters.

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.
Director
Joined: 01 Jan 2008
Posts: 605

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25 Jul 2008, 18:25
arjtryarjtry wrote:
A rectangular area is covered with a rectangular rug. If the respective sides of two rectangles are parallel to each other and have a distance of 5cm, what is the area of the large rectangle?
(1) The length of the rug is twice as long as the width of the rug.
(2) The area of the rug is 18 square centimeters.

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.

length of large rectangle = x, width = y: question what is x*y?
length of the rug = x - 5, width y - 5 //of course x > 5, y > 5

1: y-5 = 2*(x-5) -> insufficient (x,y) = (6,7) -> area = 42, (x,y) = (7,9) -> area = 63 -> insufficient
2: (x-5)*(y-5) = 18 -> insufficient (x,y) = (7,14) -> area = 98, (x,y) = (8,11) -> area = 88 -> insufficient

1&2: put y-5 in the second equation -> 2*(x-5)^2 = 18 -> (x-5)^2 = 9 -> |x-5| = 3 -> x = 8 or x = 2 // since x >5 -> x = 8 is the only solution -> y can be calculated from equation 1 -> sufficient -> C
Current Student
Joined: 11 May 2008
Posts: 552

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25 Jul 2008, 18:37
but how can one assume that the floor is the larger rectangle... why cant the carpet be larger?
alsoyou have said the surrounding width is 5, so the dimensions shoud be y-10, and x- 10 ..
is it right?

Last edited by arjtryarjtry on 25 Jul 2008, 18:40, edited 1 time in total.
Director
Joined: 01 Jan 2008
Posts: 605

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25 Jul 2008, 18:39
arjtryarjtry wrote:
but how can one assume that the floor is the larger rectangle... why cant the carpet be larger?
also the width is 5, so the length shoud be y-10, and x- 10 ..
is it right?

you are correct, it should've been x-10 and y-10, not x-5 and y-5. The answer stands though ... I think it's reasonable to assume that the rug is smaller.
Senior Manager
Joined: 09 Oct 2007
Posts: 460

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25 Jul 2008, 18:44
I agree on C.

From 1: w=2h. INSUFF

From 2: rug's area = 30. No information about dimensions. This could be 6*3, or 18*1.

Together: 3w=18 ==> w=6, h=3. Enough to find the room's area.
Current Student
Joined: 11 May 2008
Posts: 552

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25 Jul 2008, 18:51
it says rect area. why is everybody taking that the rug is of smaller area?
im asking bcos , these are the traps set in the exam.
someone clarify
VP
Joined: 17 Jun 2008
Posts: 1329

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25 Jul 2008, 20:43
arjtryarjtry wrote:
A rectangular area is covered with a rectangular rug. If the respective sides of two rectangles are parallel to each other and have a distance of 5cm, what is the area of the large rectangle?
(1) The length of the rug is twice as long as the width of the rug.
(2) The area of the rug is 18 square centimeters.

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.

IMO C
(1)=> dimentions of rug without values hence insufficient
(2)=> area of rug but no value of l,w of rug hence not a help => insufficient
(1) and (2) => for rug ,length =6,w=3 again distance is 5 cm between sides hence ru is smaller than rect area,now l+10,w+10 dimentions of rect area hence can be calculated successfully => sufficient -> IMO C
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Senior Manager
Joined: 09 Oct 2007
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26 Jul 2008, 08:45
Here's why:
A rectangular area is covered with a rectangular rug. If the respective sides of two rectangles are parallel to each other and have a distance of 5cm, what is the area of the large rectangle?
Director
Joined: 13 Nov 2003
Posts: 782
Location: BULGARIA

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26 Jul 2008, 10:11
Hi,
I see that the answer leans to C but IMO the ans is B
No mater what the ratio of the sides of the smaller rectangle we add 5 cm and will determine the sides of the bigger one. So we can find the area of the bigger rectangle
Senior Manager
Joined: 09 Oct 2007
Posts: 460

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26 Jul 2008, 19:13
BG wrote:
Hi,
I see that the answer leans to C but IMO the ans is B
No mater what the ratio of the sides of the smaller rectangle we add 5 cm and will determine the sides of the bigger one. So we can find the area of the bigger rectangle

Not really, because Stat. 2 only gives you the area of 18, which can be a result of 6 * 3, or simply 18 * 1. Therefore, inssufficient on its own.

For example, if you take 18*1 as the measures of the rug, then the measures of the room would be 28*11, giving you an area of 308. However, if you use both statements the are of the room would be 16*13, giving you an area of 208.\

At least that's what I think
Re: nice one....   [#permalink] 26 Jul 2008, 19:13
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# A rectangular area is covered with a rectangular rug. If the

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