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by Gurpinder » Fri Sep 17, 2010 10:55 am
Image

[spoiler]can someone please explain how you would calculate the area of the rectangle.

i understand that the width is 6. [/spoiler]
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by euro » Fri Sep 17, 2010 11:08 am
Gurpinder wrote:Image

[spoiler]can someone please explain how you would calculate the area of the rectangle.

i understand that the width is 6. [/spoiler]

Dia of circle = 16 = WY
Therefore, radius = OW = 8
This is sufficient to find area of circle. We need to determine if area of rectangle can be computer or not

Statement (1) WZ=OW
OW = radius of circle = 8 = OZ
Therefore, Triangle OWZ is equilateral with side = 8. Hence rectangle WXYZ is a square whose side = 8.
Statement (1) is SUFFICIENT

Statement (2) doesn't tell us anything about the dimensions of rectangle and is INSUFFICIENT

Answer is option (A) statement (1) alone is sufficient
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by goyalsau » Fri Sep 17, 2010 12:18 pm
nice work,
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by sumit.sinha » Sat Sep 18, 2010 5:01 am
euro wrote:
Gurpinder wrote:Image

[spoiler]can someone please explain how you would calculate the area of the rectangle.

i understand that the width is 6. [/spoiler]

Dia of circle = 16 = WY
Therefore, radius = OW = 8
This is sufficient to find area of circle. We need to determine if area of rectangle can be computer or not

Statement (1) WZ=OW
OW = radius of circle = 8 = OZ
Therefore, Triangle OWZ is equilateral with side = 8. Hence rectangle WXYZ is a square whose side = 8.
Statement (1) is SUFFICIENT

Statement (2) doesn't tell us anything about the dimensions of rectangle and is INSUFFICIENT

Answer is option (A) statement (1) alone is sufficient
@Euro - from Statement (1) rectangle WXYZ is not a square whose side = 8. Rectangle WXYZ has sides 8 and 8rt3.
But still Statement (1) is sufficient and (2) isn't. So Answer is (A).
Cheers,
Sumit
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by Gurpinder » Sat Sep 18, 2010 6:45 am
euro wrote: Dia of circle = 16 = WY
Therefore, radius = OW = 8
This is sufficient to find area of circle. We need to determine if area of rectangle can be computer or not

Statement (1) WZ=OW
OW = radius of circle = 8 = OZ
Therefore, Triangle OWZ is equilateral with side = 8. Hence rectangle WXYZ is a square whose side = 8.
Statement (1) is SUFFICIENT

Statement (2) doesn't tell us anything about the dimensions of rectangle and is INSUFFICIENT

Answer is option (A) statement (1) alone is sufficient
I see that (B) is not sufficient. I can also follow you up the point where you get 2 of the sides of the triangle to be 8. But how does this help you calculate the area of the rectangle? I am not sure about that!

Please explain!
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by debmalya_dutta » Sat Sep 18, 2010 7:07 am
I see that (B) is not sufficient. I can also follow you up the point where you get 2 of the sides of the triangle to be 8. But how does this help you calculate the area of the rectangle? I am not sure about that!
Please explain
Just as folks above have pointed out already ,you know that OW = OZ = WZ .. You know the diameter XZ = 16 which is nothing but 2 OZ because in a rectangle the diagnols bisect each other ... So you have OW = OZ = WZ = 8 (since 2 OZ = 8)
Since you have found XZ and WZ , you can find the area of triangle XZW ... also in rectangle , area(XZY) = area (XYZ) because diagnol cuts the rectangle into 2 triangles of same area... So basically you can find the area of the complete rectangle....

You can also find the area of the circle because you have the diameter

so rea of shaded region = area of circle - area of rectangle....So , finally , you can determine the area of the shaded region
@Deb
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by Gurpinder » Sat Sep 18, 2010 8:12 am
debmalya_dutta wrote:
I see that (B) is not sufficient. I can also follow you up the point where you get 2 of the sides of the triangle to be 8. But how does this help you calculate the area of the rectangle? I am not sure about that!
Please explain
Just as folks above have pointed out already ,you know that OW = OZ = WZ .. You know the diameter XZ = 16 which is nothing but 2 OZ because in a rectangle the diagnols bisect each other ... So you have OW = OZ = WZ = 8 (since 2 OZ = 8)
Since you have found XZ and WZ , you can find the area of triangle XZW ... also in rectangle , area(XZY) = area (XYZ) because diagnol cuts the rectangle into 2 triangles of same area... So basically you can find the area of the complete rectangle....

You can also find the area of the circle because you have the diameter

so rea of shaded region = area of circle - area of rectangle....So , finally , you can determine the area of the shaded region
Thx Deb. I was thinking about the diagonal as well.

So if we were to find the actual area, since we have hypotenuse = 16 and one side = 8, we would use the p. theorem to find the third side right? and then calculate the area, and then double that area and that would be the area for the rectangle?

What would you say would be the difficulty lvl of this question?
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by debmalya_dutta » Sat Sep 18, 2010 8:29 am
@gurpinder - no idea :) I am still getting a grasp of the whole GMAT thing..
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by sumit.sinha » Sat Sep 18, 2010 8:37 am

What would you say would be the difficulty lvl of this question?
500-600 level or maybe 600-700, but definitely not 700-800 :P
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by euro » Sat Sep 18, 2010 9:01 am
sumit.sinha wrote: @Euro - from Statement (1) rectangle WXYZ is not a square whose side = 8. Rectangle WXYZ has sides 8 and 8rt3.
But still Statement (1) is sufficient and (2) isn't. So Answer is (A).
@ Sumit
Thanks for correcting me. The rectangle WXYZ is actually not a square. Had it been a square, then the triangle would not have been an equilateral triangle. :)
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