Data Sufficiency

BTGModeratorVI wrote: ↑

Mon May 25, 2020 7:29 am

What is the degree measure of the largest angle in triangle PQR ?

(1) The degree of measure of angle P is 95.
(2) triangle PQR is isosceles.

Answer: A
Source: GMATprep

Target question: What is the degree measure of the largest angle in ΔPQR?

Statement 1: The degree of measure of ∠P is 95.
APPROACH #1: Logic
Since angles in a triangle add to 180 degrees, it's impossible for any other angles to be greater than 95 degrees (otherwise the sum of the three angles will be greater than 180 degrees)
So it must be the case that 95 degrees is the largest angle in ΔPQR

APPROACH #2: Algebra
Since angles in a triangle must add to 180 degrees, we know that ∠P + ∠Q + ∠R = 180
Substitute to get: 95 + ∠Q + ∠R = 180
Subtract 95 from both sides to get: ∠Q + ∠R = 85
If the SUM of ∠Q and ∠R is 85, neither angle can be greater than 85.
So it must be the case that 95 degrees is the measure of the largest angle in ΔPQR

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ΔPQR is isosceles.
There are tons of isosceles triangles that satisfy statement 2. Here are two:
Case a: ΔPQR has angle measurements 30-30-120. In this case, the answer to the target question is 120 degrees is the measure of the largest angle in ΔPQR
Case b: ΔPQR has angle measurements 40-40-100. In this case, the answer to the target question is 100 degrees is the measure of the largest angle in ΔPQR
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent