In triangle PQR, the measure of angle P is 30° more than twice the measure of angle Q. What is the measure of angle R?
(1) PQ = QR
(2) The measure of angle P is 78°.
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Data sufficiency
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Hi Newaz111,
This DS question is based completely on your knowledge of triangle rules.
We're told that, in triangle PQR, Angle P is 30 degrees MORE than TWICE the measure of Angle Q. We're asked for the measure of Angle R.
Fact 1: PQ = QR
This tells us the the triangle is ISOSCELES, and that Angle P = Angle R. By extension, Angle R is ALSO 30 degrees more than twice the measure of Angle Q.
Thus, our 3 angles are...
P = 30 + 2Q
Q
R = 30 + 2Q
Total = 180 degrees = 60 + 5Q. With this, we can solve for Q, which means we can solve for P and R (the angles end up as Q = 24, P = 78 and R = 78, but that math is unnecessary).
Fact 1 is SUFFICIENT.
Fact 2: Angle P = 78
With this, we can figure out Angle Q. Then, with those 2 angles, we can figure out the remaining angle (Angle R).
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This DS question is based completely on your knowledge of triangle rules.
We're told that, in triangle PQR, Angle P is 30 degrees MORE than TWICE the measure of Angle Q. We're asked for the measure of Angle R.
Fact 1: PQ = QR
This tells us the the triangle is ISOSCELES, and that Angle P = Angle R. By extension, Angle R is ALSO 30 degrees more than twice the measure of Angle Q.
Thus, our 3 angles are...
P = 30 + 2Q
Q
R = 30 + 2Q
Total = 180 degrees = 60 + 5Q. With this, we can solve for Q, which means we can solve for P and R (the angles end up as Q = 24, P = 78 and R = 78, but that math is unnecessary).
Fact 1 is SUFFICIENT.
Fact 2: Angle P = 78
With this, we can figure out Angle Q. Then, with those 2 angles, we can figure out the remaining angle (Angle R).
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
