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m08-q31

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m08-q31 [#permalink] New post 01 Feb 2009, 07:18
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Question Stats:

39% (02:32) correct 61% (01:11) wrong based on 203 sessions
The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite to angles x, 3x, and 5x respectively, then which of the following must be true?

I. c>a+b
II. c/a/b=10/6/2
III. c^2>a^2+b^2

A. I and III only
B. II and III only
C. I only
D. II only
E. III only

Source: GMAT Club Tests - hardest GMAT questions
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Oct 2013, 07:17, edited 1 time in total.
Updated
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Re: m08-q31 [#permalink] New post 01 Nov 2012, 07:28
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Expert's post
ConkergMat wrote:
If A , B , and C are points on the plane, is AB \gt 15 ?

1. BC + AC \gt 14
2. Area of triangle ABC \lt 1

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

OA does not explain how you could get an area < 1, with side > 15?


This problem was replaced by the following question:

The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite to angles x, 3x, and 5x respectively, then which of the following must be true?

I. c>a+b
II. c/a/b=10/6/2
III. c^2>a^2+b^2


A. I and III only
B. II and III only
C. I only
D. II only
E. III only

According to the relationship of the sides of a triangle: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. Thus I and II can never be true: one side (c) can not be larger than the sum of the other two sides (a and b). Note that II is basically the same as I: if c=10, a=6 and b=2 then c>a+b, which can never be true. Thus even not considering the angles, we can see that only answer choice E (III only) is left (all other options are out because each of them has either I or II in them).

Answer: E.

Now, if interested why III is true: as the angles in a triangle are x, 3x, and 5x degrees then x+3x+5x=180 --> x=20, 3x=60, and 5x=100. Next, if angle opposite c were 90 degrees, then according to Pythagoras theorem c^2=a^+b^2, but since the angel opposite c is more than 90 degrees (100) then c is larger, hence c^2>a^+b^2.

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Senior Manager
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Re: m08-q31 [#permalink] New post 30 Oct 2013, 08:11
ConkergMat wrote:
The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite to angles x, 3x, and 5x respectively, then which of the following must be true?

I. c>a+b
II. c/a/b=10/6/2
III. c^2>a^2+b^2

A. I and III only
B. II and III only
C. I only
D. II only
E. III only

Source: GMAT Club Tests - hardest GMAT questions


In this question you just have to start with I and II. If there are both wrong you know its answer E!

For the detailed explanation, Brunel has (as usual) done the job here. His explainations are really good!

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Re: m08-q31 [#permalink] New post 21 Nov 2013, 07:41
Bunuel wrote:
ConkergMat wrote:
If A , B , and C are points on the plane, is AB \gt 15 ?

1. BC + AC \gt 14
2. Area of triangle ABC \lt 1

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

OA does not explain how you could get an area < 1, with side > 15?


This problem was replaced by the following question:

The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite to angles x, 3x, and 5x respectively, then which of the following must be true?

I. c>a+b
II. c/a/b=10/6/2
III. c^2>a^2+b^2


A. I and III only
B. II and III only
C. I only
D. II only
E. III only

According to the relationship of the sides of a triangle: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. Thus I and II can never be true: one side (c) can not be larger than the sum of the other two sides (a and b). Note that II is basically the same as I: if c=10, a=6 and b=2 then c>a+b, which can never be true. Thus even not considering the angles, we can see that only answer choice E (III only) is left (all other options are out because each of them has either I or II in them).

Answer: E.

Now, if interested why III is true: as the angles in a triangle are x, 3x, and 5x degrees then x+3x+5x=180 --> x=20, 3x=60, and 5x=100. Next, if angle opposite c were 90 degrees, then according to Pythagoras theorem c^2=a^+b^2, but since the angel opposite c is more than 90 degrees (100) then c is larger, hence c^2>a^+b^2.




Is it true for all cases the side opposite to the angle >90 in a triangle will follow the same rule c^2>a^2 + b^2 ?

:oops:

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Re: m08-q31 [#permalink] New post 21 Nov 2013, 07:42
Expert's post
rango wrote:
Bunuel wrote:
ConkergMat wrote:
If A , B , and C are points on the plane, is AB \gt 15 ?

1. BC + AC \gt 14
2. Area of triangle ABC \lt 1

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

OA does not explain how you could get an area < 1, with side > 15?


This problem was replaced by the following question:

The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite to angles x, 3x, and 5x respectively, then which of the following must be true?

I. c>a+b
II. c/a/b=10/6/2
III. c^2>a^2+b^2


A. I and III only
B. II and III only
C. I only
D. II only
E. III only

According to the relationship of the sides of a triangle: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. Thus I and II can never be true: one side (c) can not be larger than the sum of the other two sides (a and b). Note that II is basically the same as I: if c=10, a=6 and b=2 then c>a+b, which can never be true. Thus even not considering the angles, we can see that only answer choice E (III only) is left (all other options are out because each of them has either I or II in them).

Answer: E.

Now, if interested why III is true: as the angles in a triangle are x, 3x, and 5x degrees then x+3x+5x=180 --> x=20, 3x=60, and 5x=100. Next, if angle opposite c were 90 degrees, then according to Pythagoras theorem c^2=a^+b^2, but since the angel opposite c is more than 90 degrees (100) then c is larger, hence c^2>a^+b^2.




Is it true for all cases the side opposite to the angle >90 in a triangle will follow the same rule c^2>a^2 + b^2 ?

:oops:

_______________
Yes, it's true.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: m08-q31   [#permalink] 21 Nov 2013, 07:42
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