Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44644

In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
23 Feb 2015, 03:31
Question Stats:
63% (00:59) correct 37% (01:10) wrong based on 189 sessions
HideShow timer Statistics



Intern
Joined: 30 Mar 2013
Posts: 10
Location: India

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
23 Feb 2015, 04:32
1
This post received KUDOS
Let us say that the radius of the circle is 'r' If we can find that out, we will be able to find out the circumference of the circle as well.
From statement 1: We get the area of the triangle. Let us say that the perpendicular sides are a & b Then, the area is ab/2 = 16*sqrt(3) => ab = 32sqrt(3) From this, we cannot determine the value of 'r' => Statement 1 is not sufficient.
From statement 2: We get that the triangle is a 306090 triangle => Ratio of the sides is 1:sqrt(3):2 => We cannot find out the radius from this information => Statement 1 is not sufficient.
Using both the statements together, we can say that the biggest side of the triangle is 2r => The smaller sides are r and r*sqrt(3) => We can form an equation in r and the given area in statement 1 From that, we will be able to find out the value of the radius and the value of the circumference.
We can solve the question using both the statements together. Correct Answer: C



Math Expert
Joined: 02 Sep 2009
Posts: 44644

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
02 Mar 2015, 06:56
Bunuel wrote: In the diagram above, what is the circumference of the circle? (1) The area of triangle is \(16*\sqrt{3}\) (2) ∠B = 60° Kudos for a correct solution.Attachment: gsdsq_img2.png MAGOOSH OFFICIAL SOLUTION:From the diagram, we know that BC is a diameter — the special case of a triangle in a semicircle. If we can find BC, we can find the circumference. Statement #1: this gives us the area of the triangle, but the angles could be anything, and so the sides could have an array of different values. Statement #1, alone and by itself, is insufficient. Statement #2: this statement would allow us to figure out all three angles of triangle ABC, but you need a length to find a length. Without any length given, we can’t find the length of BC or the circumference. Statement #2, alone and by itself, is insufficient. Statements #1 & #2 combined: Now, with both statements, we know ABC is a 306090 triangle, and we know its area, so we could figure out the side lengths, which would allow us to figure out the diameter & circumference. Combined, the statements are sufficient. Answer = C.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 18 Oct 2013
Posts: 79
Location: India
Concentration: Technology, Finance
Schools: Duke '16, Johnson '16, Kelley '16, Tepper '16, Marshall '16, McDonough '16, Insead '14, HKUST '16, HSG '15, Schulich '15, Erasmus '16, IE April'15, Neeley '15
GMAT 1: 580 Q48 V21 GMAT 2: 530 Q49 V13 GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
26 May 2015, 09:44
1
This post was BOOKMARKED
Its the simple one
We know the area of circle but doesn't know the dimension of perpendicular and base of triangle. So A and D are out. We know the triangle is 306090 but we don't know any of the side to calculate the radii of circle. So B is out. By combining we know the all the side i.e. radii of the circle. So C is sufficient



Intern
Joined: 26 Jun 2017
Posts: 1

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
18 Dec 2017, 08:29
Statement #1: this gives us the area of the triangle, but the angles could be anything, and so the sides could have an array of different values. Statement #1, alone and by itself, is insufficient.
Statement #2: this statement would allow us to figure out all three angles of triangle ABC, but you need a length to find a length. Without any length given, we can’t find the length of BC or the circumference. Statement #2, alone and by itself, is insufficient.
Statements #1 & #2 combined: Now, with both statements, we know ABC is a , and we know its area, so we could figure out the side lengths, which would allow us to figure out the diameter & circumference. Combined, the statements are sufficient.
Answer = C.[/quote]
I'm sorry but I really dont understand why the correct answer isn't A. We know that BAC is 90 degree, and we know that the inscribed angle C is equal to 1/2 of the degree of angle B. Therefore we already know that this its a 30,60,90 triangle.



Math Expert
Joined: 02 Sep 2009
Posts: 44644

In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
18 Dec 2017, 09:51
StefXgod wrote: Statement #1: this gives us the area of the triangle, but the angles could be anything, and so the sides could have an array of different values. Statement #1, alone and by itself, is insufficient.
Statement #2: this statement would allow us to figure out all three angles of triangle ABC, but you need a length to find a length. Without any length given, we can’t find the length of BC or the circumference. Statement #2, alone and by itself, is insufficient.
Statements #1 & #2 combined: Now, with both statements, we know ABC is a , and we know its area, so we could figure out the side lengths, which would allow us to figure out the diameter & circumference. Combined, the statements are sufficient.
Answer = C.
I'm sorry but I really dont understand why the correct answer isn't A. We know that BAC is 90 degree, and we know that the inscribed angle C is equal to 1/2 of the degree of angle B. Therefore we already know that this its a 30,60,90 triangle. The highlighted part is not correct. Are you saying that all right triangles inscribed in a circle are 306090 triangles? That's not true. Inscribed angle ACB is half the measure of the central angle AOB, not another inscribed angle ABC.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 09 Nov 2016
Posts: 5
Location: India
Concentration: Marketing, General Management
GPA: 3.6

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
19 Dec 2017, 12:36
I have a silly doubt regarding the C answer.
Since now we know that together they're 30690 and the area, to further find the actual diameter, basically the sides, do we use 1/2 x B x H = 16√3 So, 1/2 x AB² x AC² = 16√3
1/2 x X² x √3X²= 16√3?



Math Expert
Joined: 02 Sep 2009
Posts: 44644

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
19 Dec 2017, 20:56



Intern
Joined: 09 Nov 2016
Posts: 5
Location: India
Concentration: Marketing, General Management
GPA: 3.6

Re: In the diagram above, what is the circumference of the circle? [#permalink]
Show Tags
20 Dec 2017, 03:53
Bunuel Thankyou. I was probably too worked out, was not thinking clearly. Thankyou though. It's pretty clear now.




Re: In the diagram above, what is the circumference of the circle?
[#permalink]
20 Dec 2017, 03:53






