This is the second post about the quantitative reasoning sections on the GRE. In the previous post, I gave an arithmetic example. Now I’m following up with a “medium” geometry question in that same “quantitative comparison” style, then a “hard” question in a multi-choice style.
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Quantity A
The area of quadrilateral ABCD
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Quantity B
40
Is Quantity A higher than B? Or vice versa? Are they the same? Or is there too little information?
When reviewing our knowledge of quadrilaterals, we remember that this shape is a kite. Kites’ properties include the following: the diagonals multiplied together equals twice the area of the figure. This would be a good lead if we had information on what a BD chord (not shown) length would be… but we don’t! So the answer will be that there is too little information.
Perhaps it’s been too long since you’ve thought about all the different quadrilaterals and their properties. It is a great idea to review those topics. Here’s one post about kites, for example.
There is also the multiple choice format in geometry. The following is an example of a “hard” question.
Parallelogram OPQR lies in the xy-plane, as shown in the second figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8,6). What are the coordinates of point R?
A. (3, 2)
B. (3,3)
C. (4,4)
D. (5, 2)
E. (6, 2)
What we know about parallelograms is that their sides are parallel, and therefore have the same slope. We are given the endpoints of PQ, so we should find the slope using the slope formula. That requires you take the difference of the Ys and put them over the difference of the Xs. This “rise over run” would be found with 6-4 over 8-2, or 2 over 6. This is the same slope for OR, since it’s parallel to PQ. So if we rise 2 and run 6 from point O, which is (0,0), then we will match answer E.
