Which of the sides of triangle PQR is the longest?
1. PQ is longer than QR.
2. The measure of angle PQR is 70 degree.
[spoiler]OA: E. Could the answer not be C?[/spoiler]
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Sides of triangle PQR. Exam pack 2
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Hi prata,
This question can be solved in a couple of different ways. The 'math' behind it is based on the following triangle rule though: "the bigger the angle, the bigger the side that's across from it"
We're asked which of the three sides of triangle PQR is the longest.
1) PQ is longer than QR
This Fact tells us that the longest side CANNOT be QR, but we're not sure whether PQ or PR is the longest (and they might actually be the same length).
Fact 1 is INSUFFICIENT
2) Angle PQR = 70 degrees
With this Fact, we now know that the other two angles must add up to 110 degrees.
IF....
both angles = 55, then PR is the longest side
either angle = 70, then there's a "tie" and two of the sides are 'longest'
either angle > 70, then the side across from that angle is longest.
Fact 2 is INSUFFICIENT
Combined, we know that:
PQ is longer than QR
Angle PQR = 70
With both Facts, we know that the two sides meet at angle PQR and angle PQR = 70. Since PQ is longer than QR, angle PRQ > angle QPR.
IF the angles are 70/60/50, then PR is longest (because it's across from the 70)
IF the angles are 70/90/20, then PQ is the longest (because it's across from the 90)
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This question can be solved in a couple of different ways. The 'math' behind it is based on the following triangle rule though: "the bigger the angle, the bigger the side that's across from it"
We're asked which of the three sides of triangle PQR is the longest.
1) PQ is longer than QR
This Fact tells us that the longest side CANNOT be QR, but we're not sure whether PQ or PR is the longest (and they might actually be the same length).
Fact 1 is INSUFFICIENT
2) Angle PQR = 70 degrees
With this Fact, we now know that the other two angles must add up to 110 degrees.
IF....
both angles = 55, then PR is the longest side
either angle = 70, then there's a "tie" and two of the sides are 'longest'
either angle > 70, then the side across from that angle is longest.
Fact 2 is INSUFFICIENT
Combined, we know that:
PQ is longer than QR
Angle PQR = 70
With both Facts, we know that the two sides meet at angle PQR and angle PQR = 70. Since PQ is longer than QR, angle PRQ > angle QPR.
IF the angles are 70/60/50, then PR is longest (because it's across from the 70)
IF the angles are 70/90/20, then PQ is the longest (because it's across from the 90)
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
