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Trapezoid, Area, Triangles
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fourteenstix
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theCodeToGMAT
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The answer would be [spoiler]{B}[/spoiler]
From question:
Draw perpendicular NA
Since NOPR is parallelogram.. then angle NRA = angle OPQ
angle A and angle Q are 90 degree
NR = OP
NA = oQ
So, they both are two identical triangles..
Statement 1:
Ar(NOPR) = 30
We cannot find value for AR from here.
INSUFFICIENT
Statement 2:
Area of OPQ is given
so Area of MNR = 2 * Ar(NAR) --> since NA is acting as a perpendicular bisector for MR.
SUFFICIENT
Answer [spoiler]{B}[/spoiler]
From question:
Draw perpendicular NA
Since NOPR is parallelogram.. then angle NRA = angle OPQ
angle A and angle Q are 90 degree
NR = OP
NA = oQ
So, they both are two identical triangles..
Statement 1:
Ar(NOPR) = 30
We cannot find value for AR from here.
INSUFFICIENT
Statement 2:
Area of OPQ is given
so Area of MNR = 2 * Ar(NAR) --> since NA is acting as a perpendicular bisector for MR.
SUFFICIENT
Answer [spoiler]{B}[/spoiler]
R A H U L
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Hi fourteenstix,
The other explanations provided are mathematically correct, but I thought I'd add a few more details to the mix. This DS question becomes a bit easy of you understand how to "break down" a weird shape into smaller shapes that aren't weird.
By definition, a parallelogram is a rectangle with two identical triangles on the sides (one is just "upside down").
By definition, a trapezoid does NOT have to be symmetrical, meaning that the two diagonal lines on the sides aren't necessarily the same length or the same angle.
In THIS question, we can see an ISOSCELES triangle on the left (the two "x" angles prove it's isosceles). We're asked to find the area of THAT triangle.
Fact 1 gives us the area of the parallelogram (A = B x H), but we don't know either dimension, so it's impossible to figure out the base or the height of the triangle that we're after. Fact 1 is INSUFFICIENT.
Fact 2 gives us the area (5) of the "right-most" triangle in the parallelogram. We can take that value and transfer it over to the "left-most" triangle of the parallelogram. If you flip that shape "down" and then "mirror-left", you'll see that this triangle makes up exactly HALF of the triangle that we're trying to figure out. By doubling the 5, we get the area of the the triangle we want (10) and we have the answer. Fact 2 is SUFFICIENT.
You're not likely to see something this layered (and based on two rare shapes) on the real GMAT, so you shouldn't spend too much time on these concepts.
GMAT assassins aren't born, they're made,
Rich
The other explanations provided are mathematically correct, but I thought I'd add a few more details to the mix. This DS question becomes a bit easy of you understand how to "break down" a weird shape into smaller shapes that aren't weird.
By definition, a parallelogram is a rectangle with two identical triangles on the sides (one is just "upside down").
By definition, a trapezoid does NOT have to be symmetrical, meaning that the two diagonal lines on the sides aren't necessarily the same length or the same angle.
In THIS question, we can see an ISOSCELES triangle on the left (the two "x" angles prove it's isosceles). We're asked to find the area of THAT triangle.
Fact 1 gives us the area of the parallelogram (A = B x H), but we don't know either dimension, so it's impossible to figure out the base or the height of the triangle that we're after. Fact 1 is INSUFFICIENT.
Fact 2 gives us the area (5) of the "right-most" triangle in the parallelogram. We can take that value and transfer it over to the "left-most" triangle of the parallelogram. If you flip that shape "down" and then "mirror-left", you'll see that this triangle makes up exactly HALF of the triangle that we're trying to figure out. By doubling the 5, we get the area of the the triangle we want (10) and we have the answer. Fact 2 is SUFFICIENT.
You're not likely to see something this layered (and based on two rare shapes) on the real GMAT, so you shouldn't spend too much time on these concepts.
GMAT assassins aren't born, they're made,
Rich
