GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 23:13 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Is triangle ABC with sides a, b and c acute angled?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  P
Joined: 03 Mar 2018
Posts: 206
Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

2
4 00:00

Difficulty:   95% (hard)

Question Stats: 22% (01:35) correct 78% (02:01) wrong based on 51 sessions

HideShow timer Statistics

Is triangle ABC with sides a, b and c acute angled?

1) Triangle with sides $$a^2$$, $$b^2$$, $$c^2$$ has an area of 140 sq cms.
2) Median AD to side BC is equal to altitude AE to side BC.

_________________
Please mention my name in your valuable replies.
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

5
2
Hiii
For those who are wondering how I relate the angle with the length of sides.
Please see the sketch.

This is a part of my personal notes.

I will post more of my notes here.
Attachments IMG-20180415-WA0036.jpg [ 129.75 KiB | Viewed 2673 times ]

_________________
General Discussion
Manager  S
Joined: 24 Mar 2018
Posts: 246
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

Can you explain why option A is correct ?
Manager  P
Joined: 03 Mar 2018
Posts: 206
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

teaserbae wrote:
Can you explain why option A is correct ?

I will post the OE after a few discussions. I will PM you the OE, if you are interested.
_________________
Please mention my name in your valuable replies.
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

5
1
itisSheldon

Very nice question, see my approach.

itisSheldon wrote:
Is triangle ABC with sides a, b and c acute angled?

1) Triangle with sides $$a^2$$, $$b^2$$, $$c^2$$ has an area of 140 sq cms.
2) Median AD to side BC is equal to altitude AE to side BC.

Attachments IMG-20180415-WA0033.jpg [ 95.24 KiB | Viewed 2649 times ]

_________________
Manager  S
Joined: 24 Mar 2018
Posts: 246
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

itisSheldon wrote:
teaserbae wrote:
Can you explain why option A is correct ?

I will post the OE after a few discussions. I will PM you the OE, if you are interested.

Yeah please PM me itisSheldon
Intern  B
Joined: 26 Mar 2018
Posts: 12
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

Hey guys! Is that kind of a joke? S=1/2*h*(a or b or c)^2=140. I completely don’t understand how you found angles relation by given S.

Posted from my mobile device
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

1
Hi
The area of triangle given as 140 is not required to solve the question.
First statement just show that it is a valid triangle with sides $$a^2, b^2, c^2.$$

As for any triangle the sum of 2 sides > third side
we get $$a^2 + b^2 > c^2$$

Now consider triangle ABC with sides a, b, c
as $$a^2 + b^2 > c^2$$, hence angle between sides a and b is acute,

and $$b^2 + c^2 >a^2$$
similarly,angle between sides b and c is acute,

and $$c^2 + a^2 > b^2$$
similarly,angle between sides c and a is acute,

Since all 3 angles of triangle is acute, Hence ABC is an acute angled triangle.

Also see the attached sketch to find how we get that the angle is acute from the relation between sides.

Iamnowjust wrote:
Hey guys! Is that kind of a joke? S=1/2*h*(a or b or c)^2=140. I completely don’t understand how you found angles relation by given S.

Posted from my mobile device

Attachments IMG-20180415-WA0036.jpg [ 129.75 KiB | Viewed 2529 times ]

_________________
Manager  P
Joined: 03 Mar 2018
Posts: 206
Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

1
OE

What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.

When is the data sufficient?
The data is sufficient if we are able to get a DEFINTE YES or DEFINITE NO as the answer.

If the statements independently or together do not provide a DEFINITE YES or DEFINITE NO, the data is NOT sufficient.

What do we know from the question stem?
The question stem states that a, b, and c are the measures of the sides of a triangle.

Key properties of a triangle
If a, b, and c are the measures of the sides of a triangle, and if 'a' is the longest side of the triangle, then

i) the triangle is acute angled if $$a^2$$ < $$b^2$$ + $$c^2$$
ii) right angled if $$a^2$$ = $$b^2$$ + $$c^2$$
iii) obtuse angled if $$a^2$$ > $$b^2$$ + $$c^2$$
Quote:
Statement 1: Triangle with sides $$a^2$$, $$b^2$$, $$c^2$$ has an area of 140 sq cms.

The statement provides us with one valuable information: we can form a triangle with sides $$a^2$$, $$b^2$$, $$c^2$$

For any triangle we know that sum of two sides is greater than the third side.

So, we can infer that $$a^2$$ < $$b^2$$ + $$c^2$$.

The inequality above is the condition to be met if the triangle with sides a, b and c were to be an acute triangle.
So Statement 1 itself is sufficient.
Quote:
Statement 2: Median AD to side BC is equal to altitude AE to side BC.

Equilateral and Isosceles triangle properties
i) For an equilateral triangle, medians to the sides of the triangle are the corresponding altitudes. i.e., the median and altitude of all 3 sides are coincident lines.

ii) For an isosceles triangle, the median to the side whose measure is different is the altitude to that side. i.e., only one median is the same as the altitude.

From statement 2, we can infer that the triangle is either equilateral or isosceles.
An equilateral triangle is definitely an acute angled triangle. However, an isosceles triangle need not be an acute angled triangle.

So Statement 2 is not sufficient

gmatbusters has explained it well _________________
Please mention my name in your valuable replies.
Manager  G
Joined: 30 Mar 2017
Posts: 127
GMAT 1: 200 Q1 V1 Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

i dont agree with the above explanations for A. here's why:

we're given a triangle with sides $$a^2, b^2, c^2$$
so $$a^2+b^2>c^2$$ just means that the sum of 2 legs of the triangle is greater than the 3rd leg, which is true for every triangle (acute, obtuse, right). this specific triangle is acute if $$a^4+b^4>c^4$$

Statement 1
Sides are $$a^2, b^2, c^2$$ and area is 140
We can make our lives simpler and assume the sides are x,y,z. I think the exponents are only there to distract us.
We can vary the sides/angles as we like, while keeping the same area.
Not sufficient.
As an example, if the triangle is equilateral (and thus acute), then the area is $$140 = x^2\sqrt{3}/4$$. There's some x that fits the equation, thus it's possible that the triangle is acute. If the triangle is a right isosceles triangle (and thus not acute), then the area is $$140=\frac{1}{2}x^2$$. There's some x that fits the equation, thus it's possible that the triangle is not acute.

Statement 2
I like the explanations above. Triangle can be isosceles (and acute, obtuse, or right) or equilateral.
Not sufficient.

Combining both statements
We can use the same 2 examples in Statement 1.
Not sufficient

Retired Moderator V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

1
Hi I would be happy to clear your doubt...

You are right that for the triangle given in statement 1, a^2+b^2>c^2, this is true for all triangle whether it is acute angled, right angled or obtuse angled.

But we are using this inequality for triangle ABC which has sides a,b,c.

Now in a triangle with sides a,b,c, if a^2+b^2>c^2, we know that the angle between a and b is acute.
Similarly we can prove that angle between b and C is acute.
And finally angle between C and a is acute.
Hence the triangle ABC is acute angled triangle.

aserghe1 wrote:
i dont agree with the above explanations for A. here's why:

we're given a triangle with sides $$a^2, b^2, c^2$$
so $$a^2+b^2>c^2$$ just means that the sum of 2 legs of the triangle is greater than the 3rd leg, which is true for every triangle (acute, obtuse, right). this specific triangle is acute if $$a^4+b^4>c^4$$

Statement 1
Sides are $$a^2, b^2, c^2$$ and area is 140
We can make our lives simpler and assume the sides are x,y,z. I think the exponents are only there to distract us.
We can vary the sides/angles as we like, while keeping the same area.
Not sufficient.
As an example, if the triangle is equilateral (and thus acute), then the area is $$140 = x^2\sqrt{3}/4$$. There's some x that fits the equation, thus it's possible that the triangle is acute. If the triangle is a right isosceles triangle (and thus not acute), then the area is $$140=\frac{1}{2}x^2$$. There's some x that fits the equation, thus it's possible that the triangle is not acute.

Statement 2
I like the explanations above. Triangle can be isosceles (and acute, obtuse, or right) or equilateral.
Not sufficient.

Combining both statements
We can use the same 2 examples in Statement 1.
Not sufficient

_________________
Manager  G
Joined: 30 Mar 2017
Posts: 127
GMAT 1: 200 Q1 V1 Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

gmatbusters wrote:
Hi I would be happy to clear your doubt...

You are right that for the triangle given in statement 1, a^2+b^2>c^2, this is true for all triangle whether it is acute angled, right angled or obtuse angled.

But we are using this inequality for triangle ABC which has sides a,b,c.

Now in a triangle with sides a,b,c, if a^2+b^2>c^2, we know that the angle between a and b is acute.
Similarly we can prove that angle between b and C is acute.
And finally angle between C and a is acute.
Hence the triangle ABC is acute angled triangle.

aserghe1 wrote:
i dont agree with the above explanations for A. here's why:

we're given a triangle with sides $$a^2, b^2, c^2$$
so $$a^2+b^2>c^2$$ just means that the sum of 2 legs of the triangle is greater than the 3rd leg, which is true for every triangle (acute, obtuse, right). this specific triangle is acute if $$a^4+b^4>c^4$$

Statement 1
Sides are $$a^2, b^2, c^2$$ and area is 140
We can make our lives simpler and assume the sides are x,y,z. I think the exponents are only there to distract us.
We can vary the sides/angles as we like, while keeping the same area.
Not sufficient.
As an example, if the triangle is equilateral (and thus acute), then the area is $$140 = x^2\sqrt{3}/4$$. There's some x that fits the equation, thus it's possible that the triangle is acute. If the triangle is a right isosceles triangle (and thus not acute), then the area is $$140=\frac{1}{2}x^2$$. There's some x that fits the equation, thus it's possible that the triangle is not acute.

Statement 2
I like the explanations above. Triangle can be isosceles (and acute, obtuse, or right) or equilateral.
Not sufficient.

Combining both statements
We can use the same 2 examples in Statement 1.
Not sufficient

Thanks - I see where i went wrong. I got caught up in the info in statement 1 that I thought we had to find out if a triangle with sides a^2, b^2, c^2 is acute. But as the question stem clearly states, we need to find out if a triangle with sides a,b,c is acute.
Non-Human User Joined: 09 Sep 2013
Posts: 13239
Re: Is triangle ABC with sides a, b and c acute angled?  [#permalink]

Show Tags

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: Is triangle ABC with sides a, b and c acute angled?   [#permalink] 21 Jun 2019, 01:10
Display posts from previous: Sort by

Is triangle ABC with sides a, b and c acute angled?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  