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
OA: B
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Area of the triangle
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gmattesttaker2
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Hi Sri,
This DS question can actually be solved with almost no calculations, as long as you understand how the shapes "break down"
We're told that NOPR is a parallelogram. We're asked for the area of MNR (the isosceles triangle on the left side).
If you cut MNR "down the middle", then you'll have 2 triangles that are mirror-images of one another; they EACH have the SAME AREA as OPQ (the shaded region on the right). This relationship exists because of the parallelogram. A parallelogram is essentially just a rectangle with a triangle attached to one side and an identical "upside down" triangle attached to the other side. That upside-down triangle is a mirror image of exactly half of MNR.
Fact 1: The area of NOPR is 30.
This tells us the area of the parallelogram, but does not gives us the exact dimensions to figure out the areas of any of the triangles.
Fact 1 is INSUFFICIENT
Fact 2: The area of the shaded region is 5
With this information, we know that the two smaller triangles that make up MNR would each have an area of 5. Thus, the total area of MNR is 10.
Fact 2 is SUFFICIENT.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This DS question can actually be solved with almost no calculations, as long as you understand how the shapes "break down"
We're told that NOPR is a parallelogram. We're asked for the area of MNR (the isosceles triangle on the left side).
If you cut MNR "down the middle", then you'll have 2 triangles that are mirror-images of one another; they EACH have the SAME AREA as OPQ (the shaded region on the right). This relationship exists because of the parallelogram. A parallelogram is essentially just a rectangle with a triangle attached to one side and an identical "upside down" triangle attached to the other side. That upside-down triangle is a mirror image of exactly half of MNR.
Fact 1: The area of NOPR is 30.
This tells us the area of the parallelogram, but does not gives us the exact dimensions to figure out the areas of any of the triangles.
Fact 1 is INSUFFICIENT
Fact 2: The area of the shaded region is 5
With this information, we know that the two smaller triangles that make up MNR would each have an area of 5. Thus, the total area of MNR is 10.
Fact 2 is SUFFICIENT.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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Let x=30.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
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.
Last edited by GMATGuruNY on Fri Sep 11, 2020 3:12 am, edited 2 times in total.
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I might be missing something here, but what leads us to assume that the triangle is isosceles?Is that just a function of the parallelogram? Thanks!GMATGuruNY wrote:Let x=30.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)
Since ∆MNR is isosceles, MNOP is a trapezoid, and NOPR is a parallelogram, the following figure is yielded:
Let x=40.
Since ∆MNR is isosceles, MNOP is a trapezoid, and NOPR is a parallelogram, the following figure is yielded:
The cases above illustrate that ∆MNS = ∆NRS = ∆OPQ.
Statement 1; The area of region NOPR is 30
It's possible that NOQR = 25 and that ∆OPQ = 5.
In this case, since ∆MNS = ∆NRS = ∆OPQ = 5, ∆MNR = ∆MNS + ∆NRS = 5+5 = 10.
It's possible that NOQR = 26 and that ∆OPQ = 4.
In this case, since ∆MNS = ∆NRS = ∆OPQ = 4, ∆MNR = ∆MNS + ∆NRS = 4+4 =8.
Since ∆MNR can be different values, INSUFFICIENT.
Statement 2: The area of the shaded region is 5.
Since ∆MNS = ∆NRS = ∆OPQ = 5, ∆MNR = ∆MNS + ∆NRS = 5+5 = 10.
SUFFICIENT.
The correct answer is B.
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The figure indicates that ∠NMR = x and that ∠NRM = x.toby001 wrote:I might be missing something here, but what leads us to assume that the triangle is isosceles?Is that just a function of the parallelogram? Thanks!
Since ∆MNR has two equal angles, it is isosceles.
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toby001
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Wow! I totally missed that, didn't even see the Xs. Thank you!GMATGuruNY wrote:The figure indicates that ∠NMR = x and that ∠NRM = x.toby001 wrote:I might be missing something here, but what leads us to assume that the triangle is isosceles?Is that just a function of the parallelogram? Thanks!
Since ∆MNR has two equal angles, it is isosceles.
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Solution:gmattesttaker2 wrote: ↑Mon May 19, 2014 7:03 pmHello,
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
OA: B
Since NOPR is a parallelogram, angle OPQ and angle NRM are equal in measure. Furthermore, since triangle MNR is isosceles, the height drawn from vertex N to base MR divides the triangle into two congruent right triangles and each of these right triangles will have the same area as triangle OPQ. Therefore, if we know the area of triangle OPQ, then we can determine the area of triangle MNR.
Statement One Only:
The area of NOPR is 30.
Knowing the area of the parallelogram doesn’t give us enough information to determine the area of triangle MNR. Statement one alone is not sufficient.
Statement Two Only:
The area of the shaded region is 5.
The area of the shaded region is the area of triangle OPQ. Therefore, the area triangle MNR is twice as much, or 10. Statement two alone is sufficient.
Answer: B
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