OG In the xy-plane above is angle QPR a right angle
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Remember: on the GMAT, we cannot trust that figures are drawn accurately. So even though the diagram makes it look like QPR is a right angle, we need to definitively prove it.
Statement 1
If P and Q have the same x-coordinate, we know that P is directly above Q, making PQ parallel to the y-axis and perpendicular to the x-axis. However, this statement tells us nothing about point R. Point R could be directly horizontal from P, making PR parallel to the x-axis, perpendicular to the y-axis, and thus perpendicular to PQ. This would mean that QPR is a right angle. HOWEVER, given that we can't trust the figure to be drawn accurately, point R could be way higher than P (making QPR acute) or way lower than P (making QPR obtuse). We don't know. Insufficient.
Statement 2
If P and R have the same y-coordinate, making PR parallel to the x-axis and perpendicular to the y-axis ... but now we don't know anything about point Q - Q could be far to either the right or left of P, making our angle either acute or obtuse respectively. Insufficient.
BOTH
When we combine the two statements, we have what we need to know: PQ and PR are perpendicular, which means that the angle they form (PQR) is 90 degrees. Sufficient.
Statement 1
If P and Q have the same x-coordinate, we know that P is directly above Q, making PQ parallel to the y-axis and perpendicular to the x-axis. However, this statement tells us nothing about point R. Point R could be directly horizontal from P, making PR parallel to the x-axis, perpendicular to the y-axis, and thus perpendicular to PQ. This would mean that QPR is a right angle. HOWEVER, given that we can't trust the figure to be drawn accurately, point R could be way higher than P (making QPR acute) or way lower than P (making QPR obtuse). We don't know. Insufficient.
Statement 2
If P and R have the same y-coordinate, making PR parallel to the x-axis and perpendicular to the y-axis ... but now we don't know anything about point Q - Q could be far to either the right or left of P, making our angle either acute or obtuse respectively. Insufficient.
BOTH
When we combine the two statements, we have what we need to know: PQ and PR are perpendicular, which means that the angle they form (PQR) is 90 degrees. Sufficient.
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Hi All,
We're given a triangle in the xy-plane. We're asked if the angle QPR a right angle. This is a YES/NO question. When dealing with pictures in DS questions, it's important to note that the picture is NOT NECESSARILY drawn to scale. Thus, we have to rely on FACTS to answer the given question - and not the picture that we've been given.
1) Points P and Q have the same X-coordinate.
With the information in Fact 1, we know that segment PQ is parallel to the Y-axis (the segment goes 'straight-up-and-down'), but we don't know where point R is relative to this segment, so there's no way to know whether we have a right angle or not.
Fact 1 is INSUFFICIENT
2) Points P and R have the same Y-coordinate.
With the information in Fact 2, we know that segment PR is parallel to the X-axis (the segment goes 'straight-left-to-right'), but we don't know where point Q is relative to this segment, so there's no way to know whether we have a right angle or not.
Fact 2 is INSUFFICIENT
Combined, we know:
-PQ is parallel to the Y-axis
-PR is parallel to the X-axis
By definition, since we have a triangle with legs that are parallel to the 2 axes on a graph (and thus, perpendicular to one another), then we ARE dealing with a right triangle - so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're given a triangle in the xy-plane. We're asked if the angle QPR a right angle. This is a YES/NO question. When dealing with pictures in DS questions, it's important to note that the picture is NOT NECESSARILY drawn to scale. Thus, we have to rely on FACTS to answer the given question - and not the picture that we've been given.
1) Points P and Q have the same X-coordinate.
With the information in Fact 1, we know that segment PQ is parallel to the Y-axis (the segment goes 'straight-up-and-down'), but we don't know where point R is relative to this segment, so there's no way to know whether we have a right angle or not.
Fact 1 is INSUFFICIENT
2) Points P and R have the same Y-coordinate.
With the information in Fact 2, we know that segment PR is parallel to the X-axis (the segment goes 'straight-left-to-right'), but we don't know where point Q is relative to this segment, so there's no way to know whether we have a right angle or not.
Fact 2 is INSUFFICIENT
Combined, we know:
-PQ is parallel to the Y-axis
-PR is parallel to the X-axis
By definition, since we have a triangle with legs that are parallel to the 2 axes on a graph (and thus, perpendicular to one another), then we ARE dealing with a right triangle - so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich