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555-605 Level|   Geometry|               
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Bunuel
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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:

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Bunuel

In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as indicated. Do ΔOPQ and ΔQRS have equal areas?

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


DS71602.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1354.png

Using the diagram, we see that both triangles have a height of 3. If we can determine that the bases the same, they would have the same area. We also see that the base of triangle OPQ is c and the base of triangle QRS is d - c.

Statement One Alone:

b = 2a

Knowing that b = 2a is not enough to determine the base of either triangle. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

d = 2c

Since d = 2c, the base of triangle QRS is 2c - c = c, so the bases of the two triangles are equal and thus the area of the triangles is equal.

Answer: B
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In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as indicated. Do ΔOPQ and ΔQRS have equal areas?

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

Solve the Qn. first before going to options.
Does Areas are equal ?
If area are equal means : CX3 =(D-C)X3
C= D/2 . The actual question is whether C=D/2.

Only option 2 gives this .
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Bunuel

In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as indicated. Do ΔOPQ and ΔQRS have equal areas?

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


DS71602.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1354.png

Wanna make solving the Official Questions interesting???


Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
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Answer: Option B

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I got bogged down by statement (1) - isn't b=2a factually impossible? Wouldn't 2a be where the right leg of triangle P hits the X-axis?
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Hi GK002,

With DS questions, it's important to remember that any included pictures are not necessarily 'drawn to scale' (meaning that the exact shapes involved might be significantly different from how they appear in the prompt). We can trust whatever numbers and descriptions that we are given though.

From the drawing, we know that both Point R and Point P have a Y-coordinate of 3; this means that both points have the SAME HEIGHT.

Fact 1 tells us that B = 2A, which gives us a way to relate the relative values of the X-coordinate of each of those points. For example:

IF... A = 1, then B = 2 and the coordinates are (1,3) and (2,3)
IF... A = 2, then B = 4 and the coordinates are (2,3) and (4,3)
IF... A = 3, then B = 6 and the coordinates are (3,3) and (6,3)
Etc.

We have no idea where Points Q and S are though - and that information is necessary to determine the bases of those two triangles - and whether the triangles have the same area or not.

GMAT assassins aren't born, they're made,
Rich
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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