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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.

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&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

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.

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.

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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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?

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

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.\