It is currently 22 Nov 2017, 19:03

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is the triangle ABC, right angled at B?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 29 Nov 2011
Posts: 81

Kudos [?]: 381 [3], given: 37

Is the triangle ABC, right angled at B? [#permalink]

### Show Tags

09 Feb 2012, 18:40
3
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

48% (00:53) correct 52% (01:10) wrong based on 153 sessions

### HideShow timer Statistics

Is the triangle ABC, right angled at B?

(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.
[Reveal] Spoiler: OA

Kudos [?]: 381 [3], given: 37

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [2], given: 12403

### Show Tags

09 Feb 2012, 19:03
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

Hope it's clear.
_________________

Kudos [?]: 133076 [2], given: 12403

Manager
Joined: 14 Jan 2013
Posts: 151

Kudos [?]: 383 [0], given: 30

Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)

### Show Tags

03 Jul 2013, 14:59
Bunuel wrote:
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.

Hope it's clear.

Bunuel,

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

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

http://gmatclub.com/forum/percentages-700-800-level-questions-130588.html

http://gmatclub.com/forum/700-to-800-level-quant-question-with-detail-soluition-143321.html

Kudos [?]: 383 [0], given: 30

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [0], given: 12403

### Show Tags

03 Jul 2013, 23:41
Mountain14 wrote:
Bunuel wrote:
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.

Hope it's clear.

Bunuel,

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

_________________

Kudos [?]: 133076 [0], given: 12403

Senior Manager
Joined: 13 May 2013
Posts: 459

Kudos [?]: 202 [0], given: 134

Re: Is the triangle ABC, right angled at B? [#permalink]

### Show Tags

10 Dec 2013, 09:16
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

Kudos [?]: 202 [0], given: 134

Manager
Joined: 01 Jun 2015
Posts: 164

Kudos [?]: 36 [0], given: 102

Location: India
GMAT 1: 620 Q48 V26
Re: Is the triangle ABC, right angled at B? [#permalink]

### Show Tags

24 Mar 2017, 04:37
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".

Kudos [?]: 36 [0], given: 102

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [0], given: 12403

Re: Is the triangle ABC, right angled at B? [#permalink]

### Show Tags

24 Mar 2017, 04:41
techiesam wrote:
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".

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

Kudos [?]: 133076 [0], given: 12403

Re: Is the triangle ABC, right angled at B?   [#permalink] 24 Mar 2017, 04:41
Display posts from previous: Sort by