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04 Jan 2013, 03:06
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:07) correct
37%
(02:25)
wrong
based on 139
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On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?
(1) b + c = 6
(2) The quadrilateral is a rectangle.
(1) b + c = 6
(2) The quadrilateral is a rectangle.
04 Jan 2013, 04:41
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trex16864
There is a problem with this question. We are given that a + c = 12 and (1) says that b + c = 6, thus a = b + 6, which implies that a > b. But the stem says that a < b. I guess it should be a > b instead of a < b.
In this case the question would be:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a > b and both a and b are positive values then what is the area of the quadrilateral?
Look at the diagram below:
Attachment:
Quadrilateral.PNG [ 9.43 KiB | Viewed 5995 times ]
(1) b + c = 6. Since a + c = 12 and b + c = 6, then a - b = 6. Area = 5*6=30. Sufficient.
(2) The quadrilateral is a rectangle. We already know that. Not sufficient.
Answer: A.
Hope it's clear.
General Discussion
My solution:
Given the information in the question we can already conclude, that the quadriliteral is a rectangle with a width of 5. We need to figure out the length of the rectangle in order to find the area.
(1) with
I) \(a + c = 12\)
II) \(b + c = 6\)
we can I) - II) => \((a-b) = 6\)
Length = Distance [(a;5) (b;5)] = Distance [(a;0) (b;0)] =
= SQR [ \((a-b)^2 + (5-5)^2\) ]
= SQR [ \(6^2 + 0^2\) ]
= 6
=> \(Area = 6 * 5 = 30\) sufficient
(2) We already know that we have a rectangle. The statement gives us no further information about the length. Not sufficent
Hence A
Given the information in the question we can already conclude, that the quadriliteral is a rectangle with a width of 5. We need to figure out the length of the rectangle in order to find the area.
(1) with
I) \(a + c = 12\)
II) \(b + c = 6\)
we can I) - II) => \((a-b) = 6\)
Length = Distance [(a;5) (b;5)] = Distance [(a;0) (b;0)] =
= SQR [ \((a-b)^2 + (5-5)^2\) ]
= SQR [ \(6^2 + 0^2\) ]
= 6
=> \(Area = 6 * 5 = 30\) sufficient
(2) We already know that we have a rectangle. The statement gives us no further information about the length. Not sufficent
Hence A
