Last visit was: 20 Nov 2025, 00:18 It is currently 20 Nov 2025, 00:18
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
ramana
User avatar
Joined: 18 Oct 2008
Last visit: 29 Mar 2011
Posts: 80
Own Kudos:
109
Given Kudos: 11
Posts: 80
Kudos: 109
M17 # 04 25 Jul 2010, 07:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Are all angles of triangle \(ABC\) smaller than 90 degrees?

1. \(2AB = 3BC = 4AC\)
2. \(AC^2 + AB^2 \gt BC^2\)

Show Spoiler
Statement (1) by itself is sufficient. S1 completely defines the shape of the triangle, although not its size. Knowing the shape of the triangle, we are able to answer the question.

Statement (2) by itself is insufficient. The inequality holds in an acute-angled triangle (the answer is "yes") but it also holds if angle \(ABC\) is right (the answer is "no").
The correct answer is A.

Any alternate explanations ?

Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests for the latest questions.
Still interested? Check out the "Best Topics" block below for better discussion and related questions.
Thank you for understanding, and happy exploring!
User avatar
jakolik
User avatar
Joined: 16 Apr 2010
Last visit: 01 Nov 2012
Posts: 140
Own Kudos:
657
Given Kudos: 12
Posts: 140
Kudos: 657
M17 # 04 25 Jul 2010, 10:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,

Regarding statement 1, the angles of a triangle are proportional to the length of the sides.
Thus the angles are in the ratio of 2,3 and 4 and are thus all less than 90 degrees.

As for statement 2, note the below:
- When the sum of the squares on two sides of a triangle is greater than the square on the third side, the same holds good for other pairs of sides as well, and the triangle is acute .
- When the sum of the squares on two sides of a triangle is equal to the square on the third side, then the triangle is right angled .
- When the sum of the squares on two sides of a triangle is less than the square on the third side, then the triangle is obtuse angled .

Each statement alone is sufficient to answer the question...


Regards,
Jack
User avatar
magnetictempest
User avatar
Joined: 24 Jun 2010
Last visit: 17 Jul 2011
Posts: 24
Own Kudos:
8
Given Kudos: 3
Location: Toronto
Concentration: Marketing - Product Management
Schools:Berkeley Haas, UCLA Anderson, NYU Stern
Posts: 24
Kudos: 8
M17 # 04 28 Jul 2010, 13:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statment 2 would need to be changed so that
side 1 ^2 + side 2 ^2 >= side 3^2

As jakolik mentioned that if the square of both smaller sides is larger than the square of the longest side, then the triangle would be acute, and the statment gives enough info on its own to answer.

I also think that each statement alone is sufficient
User avatar
agdimple333
User avatar
Joined: 24 Mar 2011
Last visit: 13 Aug 2013
Posts: 226
Own Kudos:
805
Given Kudos: 20
Location: Texas
Posts: 226
Kudos: 805
M17 # 04 16 Jul 2011, 14:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone please help me here, i am not very sure if i am missing something.

2nd statement of the question, holds true i think for the question to be correct. So it should be D.
However, A is the official answer.

So either the statement 2 needs to be changed to 'greater than equal to' for the OA to hold true. OR the OA needs to be corrected.
avatar
nimisha
avatar
Joined: 06 Feb 2011
Last visit: 12 Aug 2015
Posts: 5
Own Kudos:
31
Given Kudos: 11
Posts: 5
Kudos: 31
M17 # 04 09 Aug 2011, 21:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
2nd statement says us that the sum of squares of 2 sides (side AB and AC) is greater than the third side. This statement implies only and only that the angle contained by AB and AC is acute, i.e angle BAC is acute. Since this angle is acute, one of the other 2 angles can be greater than 90 (as in 30-30-120) or less than 90 (60-60-60) or equal to 90 (30-60-90). Thus this statement is insufficient as we are not sure whether the other angle is greater than or less than 90.

Try these triangles - AB=2, AC=root 3, BC=1 (hint: its a 30-60-90 triangle) and AB=AC=BC=5. Hope it helps.
avatar
gmat1skt
avatar
Joined: 26 Sep 2011
Last visit: 28 Mar 2012
Posts: 2
Posts: 2
Kudos: 0
M17 # 04 01 Dec 2011, 14:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here i think is a general rule

For any triangle with side a, b, c
a^2 = b^2 + c^2 - 2bc Cos(t) where t is the angle between the sides b and c

If t = 90, this is a right angled triangle and the rule becomes the pythagorus theorem.
If t < 90, then cos t > 0, => a^2 < b^2 + C^2

For a triangle to be acute, all three angles must be < 90
So the above rule must be satisfied for all three sides.

In other words, a triangle is acute if
a^2 < b^2 + C^2, b^2 < a^2 + c^2, and c^2 < a^2 + b^2

Condition 1 - does not satisfy the above condition, so we know that all three angles are not < 90

Condition 2 - satisfies one of the condition, but we do not know about the other 2. - Insufficient
User avatar
teal
User avatar
Joined: 13 May 2010
Last visit: 27 Apr 2013
Posts: 68
Own Kudos:
199
Given Kudos: 4
Posts: 68
Kudos: 199
M17 # 04 28 Jul 2012, 02:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ok so in statement 1; a unique ratio tells us that shape is fixed and hence angles are fixed but can we actually determine if it's an acute or an obtuse triangle; I mean do we need to determine the actual angles from the given ratio to prove sufficiency.

Also, using the ratio of the sides as given in statement 1, how can we determine the actual angles?
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
 [3]
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
 [3]
M17 # 04 28 Jul 2012, 03:00
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
jakolik
Hi,

Regarding statement 1, the angles of a triangle are proportional to the length of the sides.
Thus the angles are in the ratio of 2,3 and 4 and are thus all less than 90 degrees.

As for statement 2, note the below:
- When the sum of the squares on two sides of a triangle is greater than the square on the third side, the same holds good for other pairs of sides as well, and the triangle is acute .
- When the sum of the squares on two sides of a triangle is equal to the square on the third side, then the triangle is right angled .
- When the sum of the squares on two sides of a triangle is less than the square on the third side, then the triangle is obtuse angled .

Each statement alone is sufficient to answer the question...


Regards,
Jack
Show more


Regarding statement 1, "the angles of a triangle are proportional to the length of the sides."

This is definitely not true! There is no such theorem.

The so-called "sinus theorem" states that for any triangle, the following equality holds:

\(\frac{AB}{sinC}=\frac{BC}{sinA}=\frac{AC}{sinB}=2R\),
where \(A, B, C\)denote the angles of the triangle and \(R\) is the radius of the circumscribed circle. \(sin\) is the \(sinus\) function, and the value of \(sina\) is not proportional to the value of \(a\).

From statement (1) we can deduce that \(AB = 6x, BC = 4x, AC = 3x\), for certain positive \(x\). Then \(AB^2=36x^2>BC^2+AC^2=25x^2\), which means the triangle is obtuse angled, with angle C greater than 90. Therefore (1) is sufficient.

(2) is not sufficient, as it only proves that angle A is not obtuse, but nothing is known about the other two angles.

Answer A.

Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests for the latest questions.
Still interested? Check out the "Best Topics" block above for better discussion and related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
105408 posts