gmattesttaker2 wrote:Hello,
Can you please assist with this:
In the figure above, if MNOP is a trapezoid and NOPR is a parallelogram, what is the area of triangular region MNR?
1) The area of region NOPR is 30
2) The area of the shaded region is 5
Let x=30.
Since triangle MNR is isosceles, MNOP is a trapezoid, and NOPR is a parallelogram, the following figure is yielded:
Let x=40.
Since triangle MNR is isosceles, MNOP is a trapezoid, and NOPR is a parallelogram, the following figure is yielded:
The cases above illustrate that triangle MNS = triangle NRS = triangle OPQ.
Statement 1; The area of region NOPR is 30
It's possible that NOQR = 25 and that triangle OPQ = 5.
In this case, since triangle MNS = triangle NRS = triangle OPQ = 5, triangle MNR = triangle MNS + triangle NRS = 5+5 = 10.
It's possible that NOQR = 26 and that triangle OPQ = 4.
In this case, since triangle MNS = triangle NRS = triangle OPQ = 4, triangle MNR = triangle MNS + triangle NRS = 4+4 =8.
Since triangle MNR can be different values, INSUFFICIENT.
Statement 2: The area of the shaded region is 5.
Since triangle MNS = triangle NRS = triangle OPQ = 5, triangle MNR = triangle MNS + triangle NRS = 5+5 = 10.
SUFFICIENT.
The correct answer is
B.
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