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

It is currently 18 Nov 2018, 19:30

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

What is the area of an obtuse angled triangle whose two side

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

Hide Tags

Intern
Intern
avatar
Joined: 24 Jul 2011
Posts: 9
What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 09 Jul 2012, 20:43
2
1
1
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

41% (00:49) correct 59% (01:13) wrong based on 129 sessions

HideShow timer Statistics

What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

A. 24 sq units
B. 48 sq units
C. 24*root3
D. 48*root3
E. Such a triangle does not exist
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 10 Jul 2012, 01:53
5
1
ficklehead wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

A. 24 sq units
B. 48 sq units
C. 24*root3
D. 48*root3
E. Such a triangle does not exist


Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:
Attachment:
Triangle.png
Triangle.png [ 12.95 KiB | Viewed 15014 times ]
Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Current Student
User avatar
B
Joined: 28 Mar 2012
Posts: 316
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 09 Jul 2012, 20:56
ficklehead wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between
two sides is 1500?
A. 24 sq units
B. 48 sq units
C. 24*root3
D.48*root3
E. Such a triangle does not exist

Hi,

The shortcut method is to use the formula,
area = 1/2*a*b*sinC
=1/2*8*12*sin(150)
=48*sin(30)
=24

The longer method is:
Attachment:
tri.jpg
tri.jpg [ 9.43 KiB | Viewed 15051 times ]

here, AB=8, AC = 12 & angleABC=150
Find the area of triangle ADC & triangle ADB
area (ABC) = ADC - ADB

Answer (A)

Regards,
Current Student
User avatar
B
Joined: 28 Mar 2012
Posts: 316
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 10 Jul 2012, 02:35
1
Bunuel wrote:
Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

Hi Bunuel,

I agree that some topics are out of scope of GMAT, but that doesn't mean one can't use it. It is always better to learn few advanced concepts (wrt GMAT) as it allows one to quickly find the answer.
Our only struggle is with time in GMAT.

Regards,
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 10 Jul 2012, 02:45
cyberjadugar wrote:
Bunuel wrote:
Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

Hi Bunuel,

I agree that some topics are out of scope of GMAT, but that doesn't mean one can't use it. It is always better to learn few advanced concepts (wrt GMAT) as it allows one to quickly find the answer.

Regards,


Who said that one cannot use trigonometry? Sure if you know trigonometry then you CAN use it. Again: trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, if you don't know trigonometry then you absolutely don't need to waste your time on it.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 30 Apr 2011
Posts: 19
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 26 Jul 2012, 09:21
How do we know that AB=8, AC = 12? we are not given the third side. The third side can be between 4 and 20, so why not the side opposite to 150? be any number greater that 12 and less that 20?
Manager
Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 198
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 27 Jul 2012, 04:00
ashwinkumar96 wrote:
How do we know that AB=8, AC = 12? we are not given the third side. The third side can be between 4 and 20, so why not the side opposite to 150? be any number greater that 12 and less that 20?



Well, Maybe its not worded properly. It also says the included angle is 150. So the 2 sides are 12 and 8.

Kudos me if you think I deserve it :) It helps!
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Intern
Intern
avatar
Joined: 11 Jul 2012
Posts: 41
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 05 Dec 2012, 11:21
Can I ask if the image was part of the problem or if you've drawn it on your own? If you did how did you decide that AB = 8 and not 12?
Brother Karamazov
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 08 Dec 2012, 05:12
1
Ousmane wrote:
Can I ask if the image was part of the problem or if you've drawn it on your own? If you did how did you decide that AB = 8 and not 12?
Brother Karamazov


The figure was not attached to the problem. As for the sides: it doesn't matter which side we assign to be 8 or 12 (if you consider AB=12 and BC=8, you'll get the same answer).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 14 Nov 2008
Posts: 62
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 15 Aug 2013, 01:39
Bunuel wrote:
ficklehead wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

A. 24 sq units
B. 48 sq units
C. 24*root3
D. 48*root3
E. Such a triangle does not exist


Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:
Attachment:
Triangle.png
Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

.


I would like to make two quick points:

1. Once you have found out the height of the triangle (AD), which is 4 here, you could have found out the area of the required triangle(ABC) simply by multiplying half of the height AD (1/2*4) and base BC (12) instead of using such a long method of find the area of ACD and subtracting from it the area of ABD.

2. Its irrelevant whether one is memorizing/using this formula (\(1:\sqrt{3}:2\) ) or memorizing/using trigonometric tables ( Although I feel knowledge of basic trigonometry is more handy), as all these formulas are interrelated. I just feel that students should be given the choice between the two. Hence, such basic trigonometry should be included in the prep materials.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 15 Aug 2013, 01:49
agourav wrote:
Bunuel wrote:
ficklehead wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

A. 24 sq units
B. 48 sq units
C. 24*root3
D. 48*root3
E. Such a triangle does not exist


Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:
Attachment:
Triangle.png
Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

.


I would like to make two quick points:

1. Once you have found out the height of the triangle (AD), which is 4 here, you could have found out the area of the required triangle(ABC) simply by multiplying half of the height AD (1/2*4) and base BC (12) instead of using such a long method of find the area of ACD and subtracting from it the area of ABD.

2. Its irrelevant whether one is memorizing/using this formula (\(1:\sqrt{3}:2\) ) or memorizing/using trigonometric tables ( Although I feel knowledge of basic trigonometry is more handy), as all these formulas are interrelated. I just feel that students should be given the choice between the two. Hence, such basic trigonometry should be included in the prep materials.


Completely disagree.

30-60-90 and 45-45-90 triangles are "GMAT triangles", so everyone should know the relationship between their sides and not spend time going into trigonometry.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8817
Premium Member
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

Show Tags

New post 31 Oct 2018, 05:02
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: What is the area of an obtuse angled triangle whose two side &nbs [#permalink] 31 Oct 2018, 05:02
Display posts from previous: Sort by

What is the area of an obtuse angled triangle whose two side

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


Copyright

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

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

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®.