Is the triangle ABC, right angled at B?

Question

(1) Two interior angles of the triangle ABC are complementary. 
(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.

Bunuel · Accepted Answer

Is the triangle ABC, right angled at B?

(1) Two interior angles of the triangle ABC are complementary --> complementary angles are two angles that add up to 90° (whereas supplementary angles are two angles that add up to 180°). Since the sum of the angles of the triangle is 180° and two angles add up to 90° then the third angle must be 90°. Though we don't know which one. Not sufficient.

(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC. Now, the larger an angle, the longest the side opposite that angle and the shorter the median drawn to this side, basically  the shortest of the medians of the triangle is the one drawn to the longest side . From this we know that AC is the longest side and opposite the largest angle B. Still insufficient as we don't know the measure of B.

(1)+(2) From (1) one of the angles must be 90° and from (2) angle B is the largest angle, hence angle B = 90°. Sufficient.

Answer: C.

Hope it's clear.

HarveyS · Answer

Bunuel,

Can you help to draw figure for Stmt 2? I am not very clear..

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=10159

WholeLottaLove · Answer

Is the triangle ABC, right angled at B?

(1) Two interior angles of the triangle ABC are complementary.

Telling us that two angles = 90 while the third must also equal 90, but this makes no mention of which angles = 90 meaning B may or may not = 90. Insufficient.

(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.

The shortest median is drawn from the longest side to the opposite angle. Therefore, the angle opposite side AC is the longest but we still don't know it's measurement. The angle could be 80 while the other two angles are 40 and 60 respectively. Insufficient.

1+2) We know that the longest side is opposite side AC (i.e. angle B). We are also told that two angles are complementary (i.e. add up to 90.) This is important. The longest angle cannot be complementary because if it was, it would add up to 90 with another angle with the third angle having to = 90 which is impossible because it isn't the largest angle in the triangle. Angle B must = 90 on it's own while the other two angles = 90 together. Thus, the triangle is right at 90 degrees. SUFFICIENT

techiesam · Answer

Bunuel  First of all thanks for the explanation.Now I'm just asking out of the curiosity that can you post any prove of the second statement: " the shortest of the medians of the triangle is the one drawn to the longest side".

Bunuel · Answer

It's a known property and you can prove this yourself just be drawing triangles.

MrJglass · Answer

Hello pal, In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it. Now you can try drawing it.

vaibhav1221 · Answer

This question is a bit tricky because one tends to assume triangle ABC to be a right angle triangle.

Karthik740 · Answer

The answers here are amazing and noteworthy!!!

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.

Is the triangle ABC, right angled at B?

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

GMAT Data Sufficiency (DS) Questions

Is the triangle ABC, right angled at B?

Prep Toolkit

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