Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #1

30

In the figure above, ABCD is a parallelogram

In the figure above, ABCD is a parallelogram. Quantity A : The area of ABCD Quantity B : 24 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

3 Explanations

1

Emma Muhleman

Easiest way to answer this can be accomplished in about 20 seconds. Always look at the answer choices before doing a bunch of work, especially on problems like this where choice B has a single number. Use 24 as a benchmark. If we wanted to get an area of 24 or more, the height would have to be at least 6. But, as we can see, that is the other side length of the parallelogram. The only parallelogram that would have an area of 24 would have to be a rectangle of dimensions 6x4, and the further you pinch that angle labeled "C" to make is smaller and smaller, you could imagine your height diminishing to almost zero.

Feb 1, 2018 • Comment

David Recine, Magoosh Tutor

Nice strategizing, Emma; your analysis is right on. :)

1

Roshan Shrestha

I also want to show that the area is less than 24 by drawing an altitude to the side 6 instead of 4. Can you please suggest me how to do that ? Thanks

Jan 20, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Hi Roshan,

Yes, it would be possible to do that - but we would need to use trigonometry (sine, cosine, or tangent) - and those functions aren't available on the GRE calculator. So we cannot solve it this way. Let me explain why we'd need to use trigonometry! :)

Let's say we draw the height, from point D to line BC, so that the height makes a right angle with BC. The height also makes a right angle with AD.

Let's call the point where the height intersects BC point X. So we have a triangle now: DXC. We know that inside the triangle, angle D is (125-90=35). Angle X is 90, so angle C must be (180-90-35=55).

So we have a triangle with angles 35, 90, and 55. We also know one side: DC is 6.

From here, to find the length of DX (the height), we would need to use sine, cosine, or tangent. If we only know the length of one side, cannot find the length of another side without using trigonometry. (Of course, the exception is when we have a special triangle - but this is not one of the special triangles you need to memorize).

So on the GRE, you cannot solve this problem using the method you suggested, since we don't have a calculator with trig buttons.

ajay singh

we can use the idea that
sin30 < sin55 < sin60 thus 6sin55 < 6sin60
and we know sin60 = sqroot(3)/2.

thus 6* sin 55 < 6sin60 < 6

Sam Kinsman, Magoosh Tutor

Hi Ajay,

That's right! Good job :)

However, keep in mind that this is not the fastest way to solve this question. I'd suggest that you use the method shown in the video - or Emma's method (see above).

Best,
Sam

6 Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment