It is currently 27 Jun 2017, 02:39

### 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

# Are all angles of triangle ABC smaller than 90 degrees?

Author Message
TAGS:

### Hide Tags

Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 217
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

19 Mar 2012, 02:43
2
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

36% (02:18) correct 64% (01:19) wrong based on 313 sessions

### HideShow timer Statistics

Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC
(2) AC^2 + AB^2 > BC^2

m17 q04
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Jun 2013, 02:49, edited 3 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

19 Mar 2012, 04:56
6
KUDOS
Expert's post
5
This post was
BOOKMARKED
We don't need to calculate anything for this question.

Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC --> we have the ratio of the sides: AB:BC:AC=6:4:3. Now, ALL triangles with this ratio are similar and have the same fixed angles. No matter what these angles actually are, the main point is that we can get them and thus answer the question. Sufficient.

(2) AC^2 + AB^2 > BC^2 --> this condition will hold for equilateral triangle (all angles are 60 degrees) as well as for a right triangle with right angle at B or C (so in this case one angle will be 90 degrees, for example consider a right triangle: AC=5, AB=4 and BC=3). Not sufficient.

Hope it's clear.
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

02 Aug 2012, 22:46
2
KUDOS
shirisha091 wrote:
Why is the ratio 6:4:3 for AB:BC:AC? Not seeing where the 6 came from.

Divide through the given equality 2AB = 3BC = 4AC by 12 and get $$\frac{AB}{6}=\frac{BC}{4}=\frac{AC}{3}$$, which can also be written as AB:BC:AC = 6:4:3.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

VP
Joined: 24 Jul 2011
Posts: 1254
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: GMAT club Geometry Q [#permalink]

### Show Tags

19 Mar 2012, 03:09
1
KUDOS
Statement 1: 2AB = 3BC = 4AC
=> AB = 2AC and BC = 4/3 AC
=> AB^2 + BC^2 = 4AC^2 + 16/9 AC^2 = 52 AC^2/9
=> AC^2 > AB^2 + BC^2
=> Angle B is obtuse
=> All angles are not acute. Sufficient.

Statement 2: AC^2 + AB^2 > BC^2
=> Angle A is acute
But this tells us nothing about the other angles. Insufficient.

_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Manager
Joined: 12 Mar 2012
Posts: 93
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

19 Mar 2012, 10:04
1st statement can be used to calculate the angles, hence A is the answer.
The second statement doesn't give any precise info.
Manager
Joined: 13 May 2010
Posts: 122
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

01 Aug 2012, 08:07
"(1) 2AB = 3BC = 4AC --> we have the ratio of the sides: AB:BC:AC=6:4:3. Now, ALL triangles with this ratio are similar and have the same fixed angles. No matter what these angles actually are, the main point is that we can get them and thus answer the question. Sufficient."

In reference to Bunnel's explanation -

How can we get the angles from the ratio of the sides? Will the angles be in the same ratio as sides?? This is not true for 45-45-90 and 30-60-90 triangles, the angles do not have the same ratio as the sides? How would you compute the actual angles given the ratio of sides, in statement 1?
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

01 Aug 2012, 08:14
teal wrote:
"(1) 2AB = 3BC = 4AC --> we have the ratio of the sides: AB:BC:AC=6:4:3. Now, ALL triangles with this ratio are similar and have the same fixed angles. No matter what these angles actually are, the main point is that we can get them and thus answer the question. Sufficient."

In reference to Bunnel's explanation -

How can we get the angles from the ratio of the sides? Will the angles be in the same ratio as sides?? This is not true for 45-45-90 and 30-60-90 triangles, the angles do not have the same ratio as the sides? How would you compute the actual angles given the ratio of sides, in statement 1?

Please, take a look at my previous post:

m17-97962.html#p1108349
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 02 Aug 2012
Posts: 3
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

02 Aug 2012, 19:04
Why is the ratio 6:4:3 for AB:BC:AC? Not seeing where the 6 came from.
Senior Manager
Joined: 22 Nov 2010
Posts: 284
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

25 Feb 2013, 04:51
(2) AC^2 + AB^2 > BC^2 --> this condition will hold for equilateral triangle (all angles are 60 degrees) as well as for a right triangle with right angle at B or C (so in this case one angle will be 90 degrees, for example consider a right triangle: AC=5, AB=4 and BC=3). Not sufficient.

Bunuel,

Can you please explain the above mentioned statement. I am not able to understand
_________________

YOU CAN, IF YOU THINK YOU CAN

Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

26 Feb 2013, 04:03
greatps24 wrote:
(2) AC^2 + AB^2 > BC^2 --> this condition will hold for equilateral triangle (all angles are 60 degrees) as well as for a right triangle with right angle at B or C (so in this case one angle will be 90 degrees, for example consider a right triangle: AC=5, AB=4 and BC=3). Not sufficient.

Bunuel,

Can you please explain the above mentioned statement. I am not able to understand

If AC=AB=BC=1 (satisfies AC^2 + AB^2 > BC^2) --> ABC is an equilateral triangle (all angles are 60 degrees) --> all angles are less than 90 degrees.
If AC=5, AB=4 and BC=3 (satisfies AC^2 + AB^2 > BC^2) --> ABC is a right triangle --> NOT all angles are less than 90 degrees.

Hope it's clear.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 469
Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

10 Dec 2013, 10:42
Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC
(2) AC^2 + AB^2 > BC^2

A triangle where a^2 + b^2 = c^2 is a right triangle, but is there any way of determining if measures greater than or less than that (say, if a^2 + b^2 was greater than c^2) lead to a triangle having measures greater than or less than 90?

I see how 1 is sufficient. ABC will always have that exact ratio of side lengths. The triangle could be 2x3x4 or 200x300x400 but the angle measurements will always be the same.
Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

11 Dec 2013, 02:20
Expert's post
2
This post was
BOOKMARKED
WholeLottaLove wrote:
Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC
(2) AC^2 + AB^2 > BC^2

A triangle where a^2 + b^2 = c^2 is a right triangle, but is there any way of determining if measures greater than or less than that (say, if a^2 + b^2 was greater than c^2) lead to a triangle having measures greater than or less than 90?

I see how 1 is sufficient. ABC will always have that exact ratio of side lengths. The triangle could be 2x3x4 or 200x300x400 but the angle measurements will always be the same.

You can see why (2) is not sufficient here: are-all-angles-of-triangle-abc-smaller-than-90-degrees-129298.html#p1060697

As for your other question, say the lengths of the sides of a triangle are a, b, and c, where the largest side is c.

For a right triangle: $$a^2 +b^2= c^2$$.
For an acute triangle: $$a^2 +b^2>c^2$$.
For an obtuse triangle: $$a^2 +b^2<c^2$$.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 469
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

11 Dec 2013, 06:20
Bunuel wrote:
WholeLottaLove wrote:
Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC
(2) AC^2 + AB^2 > BC^2

For a right triangle: $$a^2 +b^2= c^2$$.
For an acute triangle: $$a^2 +b^2>c^2$$.
For an obtuse triangle: $$a^2 +b^2<c^2$$.

Then wouldn't 2) be sufficient? According to $$a^2 +b^2<c^2$$, AC^2 + AB^2 > BC^2 shows that the two legs combined are greater than the third implying that this is an acute triangle.
Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

11 Dec 2013, 07:39
WholeLottaLove wrote:
Bunuel wrote:
WholeLottaLove wrote:
Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB = 3BC = 4AC
(2) AC^2 + AB^2 > BC^2

For a right triangle: $$a^2 +b^2= c^2$$.
For an acute triangle: $$a^2 +b^2>c^2$$.
For an obtuse triangle: $$a^2 +b^2<c^2$$.

Then wouldn't 2) be sufficient? According to $$a^2 +b^2<c^2$$, AC^2 + AB^2 > BC^2 shows that the two legs combined are greater than the third implying that this is an acute triangle.

No, because we don't know whether BC is the largest side.
_________________
Manager
Joined: 17 Mar 2014
Posts: 70
Re: GMAT club Geometry Q [#permalink]

### Show Tags

08 May 2014, 07:08
GyanOne wrote:
Statement 1: 2AB = 3BC = 4AC
=> AB = 2AC and BC = 4/3 AC
=> AB^2 + BC^2 = 4AC^2 + 16/9 AC^2 = 52 AC^2/9
=> AC^2 > AB^2 + BC^2
=> Angle B is obtuse
=> All angles are not acute. Sufficient.

Statement 2: AC^2 + AB^2 > BC^2
=> Angle A is acute
But this tells us nothing about the other angles. Insufficient.

In the above post I think it should be
AC^2 <AB^2 +BC^2 and not AC^2 > AB^2 + BC^2 as AB^2 + BC^2 = 52 AC^2/9 > AC^2

B is acute

For angle C , taking sides as Shown below

BC= (2/3)AB
AC= (2/4)AB

so BC^2 +AC^2 = (4/9 )AB^2+(1 /4)AB ^2 = (25/36)AB^2
so BC^2 +AC^2 < AB^2 hence C is obtuse

Angle C makes it sufficient not B .

Please do correct , if something still needs attention. Thank you
Chat Moderator
Joined: 19 Apr 2013
Posts: 697
Concentration: Strategy, Healthcare
Schools: Sloan '18 (A)
GMAT 1: 730 Q48 V41
GPA: 4
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

05 Mar 2015, 11:10
Bunuel, could you explain how we will find angles when we have ratio of sides as in 1). I understand that it will have the same angles, but how can we find them?
_________________

If my post was helpful, press Kudos. If not, then just press Kudos !!!

Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

05 Mar 2015, 11:26
Ergenekon wrote:
Bunuel, could you explain how we will find angles when we have ratio of sides as in 1). I understand that it will have the same angles, but how can we find them?

Finding the angles is not our aim (and this is not what you need to know for the GMAT). The aim is to determine whether we CAN find them.
_________________
Manager
Status: Perspiring
Joined: 15 Feb 2012
Posts: 117
Concentration: Marketing, Strategy
GPA: 3.6
WE: Engineering (Computer Software)
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

28 Aug 2015, 14:36
Bunuel,

a^2 + b^2 < c^2 ------------------ (c is largest then obtuse angle)
so,
3^2 + 4^2 < 6^2 -------------------- Then we have an obtuse angle.

So statement 1 becomes insufficient,
Plz help to clarify....
Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

29 Aug 2015, 02:02
NickHalden wrote:
Bunuel,

a^2 + b^2 < c^2 ------------------ (c is largest then obtuse angle)
so,
3^2 + 4^2 < 6^2 -------------------- Then we have an obtuse angle.

So statement 1 becomes insufficient,
Plz help to clarify....

The question asks: are all angles of triangle ABC smaller than 90 degrees?

Any triangle which has the ratio of the sides 6:4:3, will be an obtuse triangle, and thus we have an YES answer to the question:
Attachments

MSP3420749f5897f2deg2000045fhi8h0c14f9e4f.gif [ 1.32 KiB | Viewed 615 times ]

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15995
Re: Are all angles of triangle ABC smaller than 90 degrees? [#permalink]

### Show Tags

14 May 2017, 02:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Are all angles of triangle ABC smaller than 90 degrees?   [#permalink] 14 May 2017, 02:24
Similar topics Replies Last post
Similar
Topics:
2 ABC is a right angle triangle, which is 90 degree at A. 6 28 Apr 2016, 08:26
13 For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 12 09 Sep 2016, 14:20
1 Are all the angles of triangle ABC smaller than 90 degrees? 3 20 Dec 2014, 22:20
2 Are all angles of triangle ABC smaller than 90 degrees? 3 02 Feb 2015, 01:35
7 Are all angles of triangle ABC smaller than 90 degrees? 3 25 Jun 2013, 02:51
Display posts from previous: Sort by