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

It is currently 23 Sep 2018, 01:33

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

Circle O is inscribed in equilateral triangle ABC, which is

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

Hide Tags

Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1231
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
GMAT ToolKit User
Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post Updated on: 25 Feb 2018, 06:49
9
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:09) correct 36% (01:59) wrong based on 409 sessions

HideShow timer Statistics

Circle O is inscribed in equilateral triangle ABC, which is itself inscribed in circle P. What is the area of circle P?

(1) The area of circle O is \(4\pi\).

(2) The area of triangle ABC is \(12\sqrt{3}\).

_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

GMAT Club Premium Membership - big benefits and savings


Originally posted by Hussain15 on 26 Jun 2010, 07:52.
Last edited by Bunuel on 25 Feb 2018, 06:49, edited 2 times in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 26 Jun 2010, 09:01
7
12
Hussain15 wrote:
Circle O is inscribed in equilateral triangle ABC, which is itself inscribed in circle P. What is the area of circle P?

(1) The area of circle O is \(4\)pie.

(2) The area of triangle ABC is \(12\sqrt{2}\).


For equilateral triangle:
• The radius of the circumscribed circle is \(R=a*\frac{\sqrt{3}}{3}\), (where \(a\) is the side of equilateral triangle);
• The radius of the inscribed circle is \(r=a*\frac{\sqrt{3}}{6}\);
• The area of equilateral triangle is \(A=a^2*\frac{\sqrt{3}}{4}\).

We are asked to calculate area of bigger circle P - \(area_P=\pi{R^2}\). Note that knowing any of the following: the side of equilateral triangle \(a\), radius of the smaller circle O (as it gives \(a\)) or the radius of P itself is sufficient to calculate area of P.

(1) The area of circle O is \(4\pi\) --> we can find \(r\) --> we can find \(a\) --> we can find \(R\). Sufficient.

(2) The area of triangle ABC is \(12\sqrt{3}\) --> we can find \(a\) --> we can find \(R\). Sufficient.

Answer: D.
_________________

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
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3458
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User Premium Member CAT Tests
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 26 Jun 2010, 09:31
3
if you don't have enough time to calculate or don't remember formulas, here is fast "intuitive" approach:

Let's imagine this highly fixed structure. If you change any linear size or area, the structure just scales. We can't change any part of the system without proportionally changing all others parts. Once you get this "intuitive" idea, any linear size or area of any part of the structure defines all other linear sizes and areas of the system. For instance, if we know the height of the triangle, it's enough to find all other parameters in the system. Both statements give us information about one of the parts of the system. So, it's D.

P.S. It's a lot of text but it took 10-20sec.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago

Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1231
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
GMAT ToolKit User
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 26 Jun 2010, 10:41
1
I wish I could understand the system approach. Perhaps its the thinking of a MBA student, which I am unable to get. ;)
I try to go through it again. Let's see!!!

Posted from my mobile device
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

GMAT Club Premium Membership - big benefits and savings

CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3458
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User Premium Member CAT Tests
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 26 Jun 2010, 14:40
1
Sorry Hussain15, it's just what I was thinking when took a look at the problem. If it doesn't work for you, just leave it.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago

Intern
Intern
avatar
Joined: 24 Nov 2008
Posts: 6
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 26 Jun 2010, 16:56
1
D it is.

If a circle is inscribed in an equilateral triangle , you can find radius if the side if a triangle /height of the triangle is given or you can find side of a triangle if radius of the inscrbed circle is given

Even if you dont remember formulas as spelled out by Bunnel..you just need to remember the above fact.
Senior Manager
Senior Manager
User avatar
Joined: 25 Feb 2010
Posts: 375
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 28 Jun 2010, 07:34
1
PriyaRai wrote:
D it is.

If a circle is inscribed in an equilateral triangle , you can find radius if the side if a triangle /height of the triangle is given or you can find side of a triangle if radius of the inscrbed circle is given

Even if you dont remember formulas as spelled out by Bunnel..you just need to remember the above fact.



Even I don't remember all the formulas used above, i was able to get the answer as D with little logic and knowledge.

Who wants to know all the formulas, some time you can do without that.

there's a saying:

Who wants to know the price of everything and value of nothing.

:)
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 10 Nov 2010, 18:51
3
walker wrote:
if you don't have enough time to calculate or don't remember formulas, here is fast "intuitive" approach:

Let's imagine this highly fixed structure. If you change any linear size or area, the structure just scales. We can't change any part of the system without proportionally changing all others parts. Once you get this "intuitive" idea, any linear size or area of any part of the structure defines all other linear sizes and areas of the system. For instance, if we know the height of the triangle, it's enough to find all other parameters in the system. Both statements give us information about one of the parts of the system. So, it's D.

P.S. It's a lot of text but it took 10-20sec.


I am myself a proponent of exactly this thinking. It makes perfect sense and takes a few seconds. And, you get very good at it with practice.
Something akin to this for the intuitively inclined:
"If there is only one way in which you can draw a geometry diagram with certain specifications, you will be able to find all other sides and angles."
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
User avatar
Joined: 14 Apr 2011
Posts: 171
Reviews Badge
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 17 Jul 2011, 13:55
Thanks for the question and the intuitive approach to solve it! I'll try to practice this approach on similar questions.
_________________

Looking for Kudos :)

Intern
Intern
avatar
Joined: 07 Mar 2011
Posts: 44
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 17 Jul 2011, 14:06
Answer D.

A) if the area of circle is given. you can (r1)of the inscribed circle and from that the sides of the triangle. Sides of triangle can give you the radius (r2) of the outer circle, enough to answer the question

B) area of triangle will give you the side and also the radius (r2) or circumscribed circle.

so answer D
Manager
Manager
avatar
Joined: 17 Mar 2014
Posts: 68
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 15 May 2014, 02:06
1
Bunuel wrote:
Hussain15 wrote:
Circle O is inscribed in equilateral triangle ABC, which is itself inscribed in circle P. What is the area of circle P?

(1) The area of circle O is \(4\)pie.

(2) The area of triangle ABC is \(12\sqrt{2}\).


For equilateral triangle:
• The radius of the circumscribed circle is \(R=a*\frac{\sqrt{3}}{3}\), (where \(a\) is the side of equilateral triangle);
• The radius of the inscribed circle is \(r=a*\frac{\sqrt{3}}{6}\);
• The area of equilateral triangle is \(A=a^2*\frac{\sqrt{3}}{4}\).

We are asked to calculate area of bigger circle P - \(area_P=\pi{R^2}\). Note that knowing any of the following: the side of equilateral triangle \(a\), radius of the smaller circle O (as it gives \(a\)) or the radius of P itself is sufficient to calculate area of P.

(1) The area of circle O is \(4\pi\) --> we can find \(r\) --> we can find \(a\) --> we can find \(R\). Sufficient.

(2) The area of triangle ABC is \(12\sqrt{2}\) --> we can find \(a\) --> we can find \(R\). Sufficient.


Answer: D.


Dear Members,

Has anyone noticed that both the statements contradict each other

From statement 1 , we get \(a = 4\sqrt3\) or \(a^2 = 48\)

from statement 2 we get \(12\sqrt2 = a^2 *\frac{\sqrt3}{4}\)

or \(a^2 = 48*\frac{\sqrt2}{sqrt3}\)

both the statements should give the same value for a and \(a^2\) ,( side of the triangle).

Let me know if I am misinterpreting anything.

Although the answer is still D, both the statements shouldn't give different values for a.
Intern
Intern
avatar
Joined: 17 May 2014
Posts: 40
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 20 May 2014, 03:37
qlx wrote:
Bunuel wrote:
Hussain15 wrote:
Circle O is inscribed in equilateral triangle ABC, which is itself inscribed in circle P. What is the area of circle P?

(1) The area of circle O is \(4\)pie.

(2) The area of triangle ABC is \(12\sqrt{2}\).


For equilateral triangle:
• The radius of the circumscribed circle is \(R=a*\frac{\sqrt{3}}{3}\), (where \(a\) is the side of equilateral triangle);
• The radius of the inscribed circle is \(r=a*\frac{\sqrt{3}}{6}\);
• The area of equilateral triangle is \(A=a^2*\frac{\sqrt{3}}{4}\).

We are asked to calculate area of bigger circle P - \(area_P=\pi{R^2}\). Note that knowing any of the following: the side of equilateral triangle \(a\), radius of the smaller circle O (as it gives \(a\)) or the radius of P itself is sufficient to calculate area of P.

(1) The area of circle O is \(4\pi\) --> we can find \(r\) --> we can find \(a\) --> we can find \(R\). Sufficient.

(2) The area of triangle ABC is \(12\sqrt{2}\) --> we can find \(a\) --> we can find \(R\). Sufficient.


Answer: D.


Dear Members,

Has anyone noticed that both the statements contradict each other

From statement 1 , we get \(a = 4\sqrt3\) or \(a^2 = 48\)

from statement 2 we get \(12\sqrt2 = a^2 *\frac{\sqrt3}{4}\)

or \(a^2 = 48*\frac{\sqrt2}{sqrt3}\)

both the statements should give the same value for a and \(a^2\) ,( side of the triangle).

Let me know if I am misinterpreting anything.

Although the answer is still D, both the statements shouldn't give different values for a.


The DS question asks for data sufficiency and not the final answer. Two statements may give two different answers or same answers is not of any merit in these questions.

Don't fall for such traps.

Cheers!!!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 20 May 2014, 04:27
mittalg wrote:
qlx wrote:
Bunuel wrote:

For equilateral triangle:
• The radius of the circumscribed circle is \(R=a*\frac{\sqrt{3}}{3}\), (where \(a\) is the side of equilateral triangle);
• The radius of the inscribed circle is \(r=a*\frac{\sqrt{3}}{6}\);
• The area of equilateral triangle is \(A=a^2*\frac{\sqrt{3}}{4}\).

We are asked to calculate area of bigger circle P - \(area_P=\pi{R^2}\). Note that knowing any of the following: the side of equilateral triangle \(a\), radius of the smaller circle O (as it gives \(a\)) or the radius of P itself is sufficient to calculate area of P.

(1) The area of circle O is \(4\pi\) --> we can find \(r\) --> we can find \(a\) --> we can find \(R\). Sufficient.

(2) The area of triangle ABC is \(12\sqrt{2}\) --> we can find \(a\) --> we can find \(R\). Sufficient.


Answer: D.


Dear Members,

Has anyone noticed that both the statements contradict each other

From statement 1 , we get \(a = 4\sqrt3\) or \(a^2 = 48\)

from statement 2 we get \(12\sqrt2 = a^2 *\frac{\sqrt3}{4}\)

or \(a^2 = 48*\frac{\sqrt2}{sqrt3}\)

both the statements should give the same value for a and \(a^2\) ,( side of the triangle).

Let me know if I am misinterpreting anything.

Although the answer is still D, both the statements shouldn't give different values for a.


The DS question asks for data sufficiency and not the final answer. Two statements may give two different answers or same answers is not of any merit in these questions.

Don't fall for such traps.

Cheers!!!


That's not true. On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.
_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 20 May 2014, 04:28
qlx wrote:
Bunuel wrote:
Hussain15 wrote:
Circle O is inscribed in equilateral triangle ABC, which is itself inscribed in circle P. What is the area of circle P?

(1) The area of circle O is \(4\)pie.

(2) The area of triangle ABC is \(12\sqrt{2}\).


For equilateral triangle:
• The radius of the circumscribed circle is \(R=a*\frac{\sqrt{3}}{3}\), (where \(a\) is the side of equilateral triangle);
• The radius of the inscribed circle is \(r=a*\frac{\sqrt{3}}{6}\);
• The area of equilateral triangle is \(A=a^2*\frac{\sqrt{3}}{4}\).

We are asked to calculate area of bigger circle P - \(area_P=\pi{R^2}\). Note that knowing any of the following: the side of equilateral triangle \(a\), radius of the smaller circle O (as it gives \(a\)) or the radius of P itself is sufficient to calculate area of P.

(1) The area of circle O is \(4\pi\) --> we can find \(r\) --> we can find \(a\) --> we can find \(R\). Sufficient.

(2) The area of triangle ABC is \(12\sqrt{2}\) --> we can find \(a\) --> we can find \(R\). Sufficient.


Answer: D.


Dear Members,

Has anyone noticed that both the statements contradict each other

From statement 1 , we get \(a = 4\sqrt3\) or \(a^2 = 48\)

from statement 2 we get \(12\sqrt2 = a^2 *\frac{\sqrt3}{4}\)

or \(a^2 = 48*\frac{\sqrt2}{sqrt3}\)

both the statements should give the same value for a and \(a^2\) ,( side of the triangle).

Let me know if I am misinterpreting anything.

Although the answer is still D, both the statements shouldn't give different values for a.


You are right. I guess the second statement should read: the area of triangle ABC is \(12\sqrt{3}\).

Edited the question. Thank you.
_________________

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

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 20 Oct 2015, 09:28
how do you solve, in theory, to come to the conclusion that radius of the circumscribed circle is a*sqrt(3)/3?
is it because the diameter will be 1/2 time of the side?
in this case, the diameter will be a/2, and R is a/4, where a is the side of the equilateral triangle.

knowing that the triangle is inscribed in a circle, we can draw 2 radii which will connect with one side of the triangle, creating a 30-30-120 triangle. Then, we can draw a perpendicular, and get 2 triangles of 30-60-90, in which the longest leg will be a/2, where a is the side of the equilateral triangle.

is my way of thinking right?
in case we know area of the small circle, we can find the side of the equilateral triangle, and thus, can find the radius of the big circle.
in case we know the area of the equilateral triangle, we can deduct that A=[S^2 sqrt(3)]/4. Now, we can find the side of the equilateral triangle, and hence, find the radius of the big circle.

I believe this is more a 700 level question :)
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 21 Oct 2015, 23:45
2
mvictor wrote:
how do you solve, in theory, to come to the conclusion that radius of the circumscribed circle is a*sqrt(3)/3?
is it because the diameter will be 1/2 time of the side?
in this case, the diameter will be a/2, and R is a/4, where a is the side of the equilateral triangle.

knowing that the triangle is inscribed in a circle, we can draw 2 radii which will connect with one side of the triangle, creating a 30-30-120 triangle. Then, we can draw a perpendicular, and get 2 triangles of 30-60-90, in which the longest leg will be a/2, where a is the side of the equilateral triangle.

is my way of thinking right?
in case we know area of the small circle, we can find the side of the equilateral triangle, and thus, can find the radius of the big circle.
in case we know the area of the equilateral triangle, we can deduct that A=[S^2 sqrt(3)]/4. Now, we can find the side of the equilateral triangle, and hence, find the radius of the big circle.

I believe this is more a 700 level question :)


Check out these posts. They discuss relations between circles and inscribed polygons (including equilateral triangle)

http://www.veritasprep.com/blog/2013/06 ... d-circles/
http://www.veritasprep.com/blog/2013/07 ... relations/

Once you understand these relations, you will jump to (D) immediately.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6227
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 22 Oct 2015, 13:32
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Circle O is inscribed in equilateral triangle ABC, which is itself inscribed in circle P. What is the area of circle P?

(1) The area of circle O is 4 pie.

(2) The area of triangle ABC is 123 √ .

In the original condition, the there is only one variable (radius), and we need one equation to solve for the question.
2 equations are given from the 2 conditions, so there is high chance (D) will be our answer; in fact, (D) is our answer.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8150
Premium Member
Re: Circle O is inscribed in equilateral triangle ABC, which is  [#permalink]

Show Tags

New post 25 Feb 2018, 05:20
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: Circle O is inscribed in equilateral triangle ABC, which is &nbs [#permalink] 25 Feb 2018, 05:20
Display posts from previous: Sort by

Circle O is inscribed in equilateral triangle ABC, which is

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

Events & Promotions

PREV
NEXT


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®.