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In the figure above, the vertices of triangle OPQ and

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In the figure above, the vertices of triangle OPQ and

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In the figure above, the vertices of triangle OPQ and triangle QRS have coordinates as indicated. Do triangle OPQ and triangle QRS have equal areas?

(1) b = 2a
(2) d = 2c

B

Source: Official Guide 2020

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Hi All,

We're told that In the figure above, the vertices of triangle OPQ and triangle QRS have coordinates as indicated. We're asked if triangle OPQ and triangle QRS have equal areas. This is a YES/NO question and is built on Geometry rules (although you might find it useful to TEST VALUES). Based on the information in the graph, BOTH triangles have a HEIGHT of 3, so for those triangles to have the SAME area, they must have the same BASE (meaning that D - C would have to equal C - 0).

(1) B = 2A

The information in Fact 1 defines the ratio of how 'spread out' the top of each triangle is from the other, but tells us nothing about the bases of the triangles. You might find it helpful to think about where Point S COULD be (while the two triangles could be identical, it's possible that Point S might be really far to the right on the graph - meaning that triangle QRS is much bigger than triangle OPQ).
Fact 1 is INSUFFICIENT

(2) D = 2C

With the information in Fact 2, you might recognize that D is exactly TWICE as far from 0 as C is, so C is exactly "in the middle" and (D - C) and (C - 0) are equal. If you don't immediately see that, then you can prove it by TESTing VALUES.

IF....
C=1 and D=2, then (D-C) = 1 and (C-0) = 1 and the answer to the question is YES.
C=1.5 and D=3, then (D-C) = 1.5 and (C-0) = 1.5 and the answer to the question is YES.
C=2 and D=4, then (D-C) = 2 and (C-0) = 2 and the answer to the question is YES.
Etc.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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