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C
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Find the cost of flooring a square room if the cost of flooring the room per square metre is Rs. 25.
(1) The square room has a veranda of uniform width of 3 metres around it.
(2) The area of the veranda is 432 square metres.
(1) The square room has a veranda of uniform width of 3 metres around it.
(2) The area of the veranda is 432 square metres.
28 Jul 2021, 04:21
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If we knew the area of the room, we could answer the question. I assume Statement 1 is trying to tell us we have a square-inside-a-square (the room is a square, then when we add on the veranda of uniform width, we get a larger square). Statement 1 tells us nothing about the size of the inside square, so isn't sufficient, and using only Statement 2, we again know nothing about the room (or even about what this veranda is, since we need to forget about Statement 1).
But using both statements, the larger the room, the larger the veranda will be, so there can only be one size of room that produces a veranda of 432 square meters, and the answer must be C. We don't need to solve anything, but if we wanted to, if the room's length is x, the veranda's is x+6 (it's extends 3 meters beyond the room in both directions). So the area of the veranda and room combined is (x+6)^2, and the area of the room is x^2, and the area only of the veranda is (x + 6)^2 - x^2 = (x + 6 + x)(x + 6 - x) = 6(2x + 6) = 12(x + 3), here using the difference of squares, and since this is equal to 432, we have
12(x + 3) = 432
x + 3 = 36
x = 33
So the area of the room is 33^2, and the cost at 25 Rs per square meter is 25*33^2.
But using both statements, the larger the room, the larger the veranda will be, so there can only be one size of room that produces a veranda of 432 square meters, and the answer must be C. We don't need to solve anything, but if we wanted to, if the room's length is x, the veranda's is x+6 (it's extends 3 meters beyond the room in both directions). So the area of the veranda and room combined is (x+6)^2, and the area of the room is x^2, and the area only of the veranda is (x + 6)^2 - x^2 = (x + 6 + x)(x + 6 - x) = 6(2x + 6) = 12(x + 3), here using the difference of squares, and since this is equal to 432, we have
12(x + 3) = 432
x + 3 = 36
x = 33
So the area of the room is 33^2, and the cost at 25 Rs per square meter is 25*33^2.
24 Aug 2021, 13:58
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lexjp1019
There are actually several issues with the wording here, so I wouldn't worry at all about whether you were able to understand it. Official GMAT questions are much more carefully worded than this one is. To answer your questions: the question asks about flooring a room. If you look only at Statement 2, it tells us that a veranda has an area of 432 m^2. A veranda is not a room, so using only Statement 2, we know nothing about the room, and can't do anything. And when you use both statements, you know you have a square room, and that room is surrounded by this veranda of 'uniform width'. It's like having a hallway that surrounds the square room, and the hallway throughout is 3 meters wide. If you draw a picture of what that looks like, you'll see you have a smaller square (the room) inside a larger square (the room and veranda together).
