In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as

Question

https://gmatclub.com/forum/download/file.php?id=47586 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 2019-04-26_1354.png

DavidTutorexamPAL · Accepted Answer

The Logical approach to this question will focus on the formula of triangular area: since both of the triangles have the same height (3),in order to compare their areas all we need to know is the lengths of their bases.
Statement (1) doesn't provide any information about the base, but statement (2) does: if d=2c,it means that since the length of OQ is c, the length of QS is 2c-c=c. So both triangles have the same base, and thus the same area. Since statement (2) was sufficient on its own, but statement (1) wasn't, the correct answer is (B).

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ZoltanBP · Answer

The y-coordinate of any point in the xy-coordinate plane measures that point's distance from the x-axis. If a triangle has one of its sides on the x-axis, then the y-coordinate of its vertex opposite this base measures the height corresponding to this base. The relevant height of each of these triangles in the figure is 3.

The original question: Is  \frac{(c-0)\cdot 3}{2}=\frac{(d-c)\cdot 3}{2}  ?
The rephrased question: Is  c=d-c  ?  \implies  Is  d=2c  ?

1) We know that  b=2a , but no information is given about  c  or  d . Thus, we can't get a definite answer to the rephrased question.  \implies   Insufficient

2) We know that  d=2c . Thus, the answer to the rephrased question is a definite Yes.  \implies   Sufficient

Answer: B

EMPOWERgmatRichC · Answer

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

ScottTargetTestPrep · Answer

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

sanjeevsinha082 · Answer

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 .

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=4tyak_NBwTw

GK002 · Answer

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?

EMPOWERgmatRichC · Answer

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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=ZFZOLRrjYLA

bumpbot · Answer

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In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as

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In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as

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