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How many of the three heights of triangle ABC do not pass inside the

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How many of the three heights of triangle ABC do not pass inside the [#permalink]

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New post 30 Mar 2017, 08:18
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How many of the three heights of triangle ABC do not pass inside the triangle?

(1) ΔABC is obtuse.

(2) The altitude of A from BC does not pass inside ΔABC.

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Re: How many of the three heights of triangle ABC do not pass inside the [#permalink]

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New post 30 Mar 2017, 08:30
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St1: ABC is obtuse --> Suppose B is the obtuse angle and BC is the base. Project BC to a point D such that D is vertically below A then AD will be the height and will lie outside the triangle. Thus, there is one height that does not pass inside the triangle.

St2: The altitude of A from BC does not pass inside ΔABC. --> Sufficient.

Answer: D
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Re: How many of the three heights of triangle ABC do not pass inside the [#permalink]

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New post 03 Apr 2017, 09:13
I did not understand this question. Diagrams please?
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Re: How many of the three heights of triangle ABC do not pass inside the [#permalink]

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New post 03 Apr 2017, 10:11
It seems like there may be some language translation issues in this problem. What are heights and altitudes in the context of triangles? Are these supposed to be lengths and angles?
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Re: How many of the three heights of triangle ABC do not pass inside the [#permalink]

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New post 03 Apr 2017, 10:14
ar500 wrote:
It seems like there may be some language translation issues in this problem. What are heights and altitudes in the context of triangles? Are these supposed to be lengths and angles?


Height and altitude are the same thing - the altitude of a triangle is the perpendicular from the base to the opposite vertex.

Check more here: https://gmatclub.com/forum/math-triangles-87197.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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How many of the three heights of triangle ABC do not pass inside the [#permalink]

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New post 03 Apr 2017, 23:32
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SOUMYAJIT_ wrote:
I did not understand this question. Diagrams please?


Attached figure for your reference. Notice that height AD lies outside the obtuse angled triangle ABC.
Attachments

Triangle.png
Triangle.png [ 4.18 KiB | Viewed 459 times ]

How many of the three heights of triangle ABC do not pass inside the   [#permalink] 03 Apr 2017, 23:32
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