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right angled at

by sanju09 » Thu Feb 09, 2012 4:37 am
Is the triangle ABC, right angled at B?
I. Two interior angles of the triangle ABC are complementary.
II. In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.





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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Feb 09, 2012 5:38 pm
sanju09 wrote:Is the triangle ABC, right angled at B?
I. Two interior angles of the triangle ABC are complementary.
II. In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
(1) Two interior angles of the triangle ABC are complementary.
If A = 30, B = 60, then C = 90. Here ABC is right angled at C.
If A = 30, C = 60, then B = 90. Here ABC is right angled at B.

So, triangle ABC may or may not be right angled at B; 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 again implies that triangle ABC may or may not be right angled at B (please see the following figures for more clarification; NOT sufficient.

Image

Combining (1) and (2), we can say that the triangle ABC is right angled at B; SUFFICIENT.

The correct answer is C.
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by sanju09 » Sat Oct 19, 2013 11:15 pm
Anurag@Gurome wrote:
sanju09 wrote:Is the triangle ABC, right angled at B?
I. Two interior angles of the triangle ABC are complementary.
II. In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
(1) Two interior angles of the triangle ABC are complementary.
If A = 30, B = 60, then C = 90. Here ABC is right angled at C.
If A = 30, C = 60, then B = 90. Here ABC is right angled at B.

So, triangle ABC may or may not be right angled at B; 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 again implies that triangle ABC may or may not be right angled at B (please see the following figures for more clarification; NOT sufficient.

Image

Combining (1) and (2), we can say that the triangle ABC is right angled at B; SUFFICIENT.

The correct answer is C.
Great explanation, Anurag, great graphics!
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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