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Is the triangle ABC, right angled at B?

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

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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.
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Re: Triangles [#permalink]

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

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Re: Triangles [#permalink]

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New post 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.

Answer: C.

Hope it's clear.

Bunuel,

Can you help to draw figure for Stmt 2? I am not very clear..
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Re: Triangles [#permalink]

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New post 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.

Answer: C.

Hope it's clear.

Bunuel,

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


Image
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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

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

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

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

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

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New post 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.
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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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Re: Is the triangle ABC, right angled at B?   [#permalink] 24 Mar 2017, 04:41
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