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

It is currently 11 Jul 2014, 04:59

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Are all angles of triangle ABC smaller than 90 degrees? (1)

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
SVP
SVP
avatar
Joined: 21 Jul 2006
Posts: 1550
Followers: 7

Kudos [?]: 169 [0], given: 1

GMAT Tests User
Are all angles of triangle ABC smaller than 90 degrees? (1) [#permalink] New post 13 Nov 2008, 01:13
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC

(2) (AC)^2 + (AB)^2 > (BC)^2














Now, the OA to this question is A. First, I thought the answer is D, but I was wrong. But I also know that any right triangle has the equation a^2+b^2 = c^2. In statement 2, we rather have a^2 + b^2 > c^2 (assuming that we have the 3 sides to be a,b,c). How come that could also be a right triangle?
Manager
Manager
avatar
Joined: 30 Sep 2008
Posts: 113
Followers: 1

Kudos [?]: 9 [0], given: 0

Re: DS: Geometry [#permalink] New post 13 Nov 2008, 01:33
From the OA you post I got the solution

(1) 2AB = 3BC = 4AC

we have cos A = (AB^2 + AC^2 - BC^2) / (2AB * AC)

from cosA, we know if A>0 or not, same with B, C => suff

(2) only know for angle A => insuff

=>D
SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1580
Followers: 11

Kudos [?]: 171 [0], given: 0

GMAT Tests User
Re: DS: Geometry [#permalink] New post 13 Nov 2008, 01:44
B is insufficient as even in right angled triangle with right angle at B, stmt2 will hold true.
SVP
SVP
avatar
Joined: 21 Jul 2006
Posts: 1550
Followers: 7

Kudos [?]: 169 [0], given: 1

GMAT Tests User
Re: DS: Geometry [#permalink] New post 13 Nov 2008, 02:40
I know at least that A is correct because if it is a right triangle, then the ratio of the sides should be either 3:4:5, 5:12:13, etc...but from statement 1, the ratio of 2:3:4 is no way the ratio of a right triangle.

my main concern is with option B, because I honestly thought that it's suff. as "no", but according to the OA, statement 2 can mean both a right triangle and a non-right triangle...how??
SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1580
Followers: 11

Kudos [?]: 171 [0], given: 0

GMAT Tests User
Re: DS: Geometry [#permalink] New post 13 Nov 2008, 02:50
tarek99 wrote:
I know at least that A is correct because if it is a right triangle, then the ratio of the sides should be either 3:4:5, 5:12:13, etc...but from statement 1, the ratio of 2:3:4 is no way the ratio of a right triangle.

my main concern is with option B, because I honestly thought that it's suff. as "no", but according to the OA, statement 2 can mean both a right triangle and a non-right triangle...how??



Look at my earlier post. Draw a triangle with obtuse angle at B. Stmt2 will still hold true.
SVP
SVP
avatar
Joined: 21 Jul 2006
Posts: 1550
Followers: 7

Kudos [?]: 169 [0], given: 1

GMAT Tests User
Re: DS: Geometry [#permalink] New post 13 Nov 2008, 03:12
scthakur wrote:
tarek99 wrote:
I know at least that A is correct because if it is a right triangle, then the ratio of the sides should be either 3:4:5, 5:12:13, etc...but from statement 1, the ratio of 2:3:4 is no way the ratio of a right triangle.

my main concern is with option B, because I honestly thought that it's suff. as "no", but according to the OA, statement 2 can mean both a right triangle and a non-right triangle...how??



Look at my earlier post. Draw a triangle with obtuse angle at B. Stmt2 will still hold true.



there's no way an obtuse will work. An obtuse angle is already more than 90 degrees. So if one of the angle is obtuse, there is simply no way that one of the remaining angles can even be 90. This is because if there is a second angle that has a 90 degrees, then the total sum of angles will be more than 180, which is impossible.
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3597
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 346

Kudos [?]: 1660 [0], given: 354

GMAT ToolKit User GMAT Tests User Premium Member
Re: DS: Geometry [#permalink] New post 13 Nov 2008, 03:13
Expert's post
Another way to think of this problem...

A) 3 sides of the triangle always fix all angles. So we even haven't to go further in order to define presence of a >90 angle.

B) Let's consider the case with huge AB and AC, and small BC. Let's ABC is near 0. Now, let's try to move in mind BC changing ABC angle from 0 to 180. It becomes obvious that we move from triangle with >90 angle at ABC~0 to triangle without >90 angle at AB=AC and again toward triangle with >90 angle at ABC~180. Moreover, duiring the movement we pass two right triangles (ABC=90 and ACB=90).

Hope this help
_________________

NEW! GMAT ToolKit 2 (iOS) / GMAT ToolKit (Android) - The must have GMAT prep app | PrepGame

Director
Director
avatar
Joined: 29 Aug 2005
Posts: 881
Followers: 7

Kudos [?]: 136 [0], given: 7

GMAT Tests User
Re: DS: Geometry [#permalink] New post 17 Nov 2008, 07:28
walker wrote:
Another way to think of this problem...

A) 3 sides of the triangle always fix all angles. So we even haven't to go further in order to define presence of a >90 angle.

B) Let's consider the case with huge AB and AC, and small BC. Let's ABC is near 0. Now, let's try to move in mind BC changing ABC angle from 0 to 180. It becomes obvious that we move from triangle with >90 angle at ABC~0 to triangle without >90 angle at AB=AC and again toward triangle with >90 angle at ABC~180. Moreover, duiring the movement we pass two right triangles (ABC=90 and ACB=90).

Hope this help

walker, your explanation is helpful. I agree with OA being A.
Re: DS: Geometry   [#permalink] 17 Nov 2008, 07:28
    Similar topics Author Replies Last post
Similar
Topics:
Are all angles of triangle ABC smaller than 90 degrees? 1. Economist 1 22 Sep 2009, 11:09
Are all angles of triangle ABC smaller than 90 degrees? 1. sondenso 1 26 May 2008, 02:43
1 Are all angles of triangle ABC smaller than 90 degrees? 1. marcodonzelli 4 02 Mar 2008, 07:55
2 Are all the angles of triangle ABC smaller than 90 degrees? bmwhype2 14 20 Dec 2007, 13:14
Are all the angles of Triangle ABC smaller than 90 degrees? bz9 7 21 Feb 2007, 03:43
Display posts from previous: Sort by

Are all angles of triangle ABC smaller than 90 degrees? (1)

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.