M16-10

Question

Is triangle  ABC  a right triangle?

(1)  \angle ABC = \angle BCA

(2)  \angle ABC = \angle CAB + 30  degrees

Bunuel · Answer

Official Solution:

Statement (1) by itself is insufficient. The triangle is isosceles but this imposes no restrictions on angle  CAB .
 
Statement (2) by itself is insufficient. Assigning different values to angle  CAB , we will get different triangles. If  CAB = 60  or  30 , the triangle is a right triangle.
 
Statements (1) and (2) combined are sufficient. S1 and S2 provide a system of three linear equations (the third equation is derived from the condition that the sum of the angles equals 180 degrees) with three unknown variables. From this system, we can find the value of each angle.

Answer: C

abhilash53 · Answer

Hello,

Can you please share how the property that all interior angles sum to 180 helps us get answer C. Thanks in advance for your help?

Bunuel · Answer

We'll have x + x + (x - 30) = 180 --> x = 70. So, the angles are 70, 70 and 40.

CPGguyMBA2018 · Answer

Since from (1) and (2) we have:
(1) B = C
(2) A+30 = B or A =B-30
and A+B+C = 180,
(B-30)+B+B = 180
3B = 210
B = 70

Since B=70, C=70, and A=40
(1)+(2) Sufficient. C.

Vikram_Katti · Answer

Question becomes much easier once you have drawn the figure.

Angle ABC, CAB and BCA can become confusing without the figure.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

M16-10

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards