Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Oct 2016, 18:19

### 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

# m08-q31

Author Message
Manager
Joined: 17 Dec 2008
Posts: 177
Followers: 2

Kudos [?]: 118 [0], given: 0

### Show Tags

01 Feb 2009, 08:18
4
This post was
BOOKMARKED
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

Last edited by Bunuel on 30 Oct 2013, 08:17, edited 1 time in total.
Updated
Math Expert
Joined: 02 Sep 2009
Posts: 35286
Followers: 6644

Kudos [?]: 85678 [6] , given: 10242

### Show Tags

01 Nov 2012, 08:28
6
KUDOS
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).

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.
_________________
Senior Manager
Status: Student
Joined: 26 Aug 2013
Posts: 265
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Followers: 2

Kudos [?]: 56 [0], given: 401

### Show Tags

30 Oct 2013, 09:11
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!
_________________

Think outside the box

Manager
Joined: 28 Apr 2013
Posts: 159
Location: India
GPA: 4
WE: Medicine and Health (Health Care)
Followers: 1

Kudos [?]: 64 [0], given: 84

### Show Tags

21 Nov 2013, 08:41
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).

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 ?

_________________

Thanks for Posting

LEARN TO ANALYSE

+1 kudos if you like

Math Expert
Joined: 02 Sep 2009
Posts: 35286
Followers: 6644

Kudos [?]: 85678 [0], given: 10242

### Show Tags

21 Nov 2013, 08:42
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).

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 ?

_______________
Yes, it's true.
_________________
Re: m08-q31   [#permalink] 21 Nov 2013, 08:42
Display posts from previous: Sort by

# m08-q31

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.