November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 419

What is the area of the shaded region above, if ABCD
[#permalink]
Show Tags
11 Jan 2014, 07:16
Question Stats:
65% (02:00) correct 35% (01:56) wrong based on 262 sessions
HideShow timer Statistics
Attachment: File comment: Geometry
ABCD.png [ 20.95 KiB  Viewed 8485 times ]
What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O? (1) The radius of the circle with center O is 4. (2) The area of triangle ADC is 32. OE To find area of shaded region, you need to find area of triangle ACD, and subtract area of unshaded region inside this triangle from it. To find area of unshaded region, you need to first draw in a line perpendicular to diameter AB of circle from center O to diagonal AC. Call this point E. This point is also one of endpoints of arc AFE. Attachment: File comment: ABCD2
ABCD2.png [ 19.07 KiB  Viewed 7238 times ]
Arc AFE and radii OA and OE bound a sector of circle O: this sector is one quarter of entire area of circle. Now, if you take area of small triangle AEO, and subtract this area from area of sector OAFE, then you have area of unshaded portion of triangle ADC. So, to solve this question, you need to find area of triangle ADC, one quarter of area of circle O, and area of small triangle AEO. To find these three areas, you need radius of circle, or length of one side of square. (1): This is exactly what we need; once we have radius of circle we can find diameter of circle which is same as a side of square and also same as each leg of right triangle ADC. So you can, with this information, solve for different areas necessary, and then solve for area of shaded region. Sufficient. (2): able to find length of height and width (which are equal to each other) of triangle ADC. Let's say that both base and height of triangle ADC = x. 32 = (½)x^2 → x = 8 You have leg lengths (which are equal) of isosceles right triangle ADC; this means that you also have diameter of circle → radius. Sufficient
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 50619

Re: What is the area of the shaded region above, if ABCD
[#permalink]
Show Tags
11 Jan 2014, 07:26
goodyear2013 wrote: Attachment: ABCD.png What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O? (1) The radius of the circle with center O is 4. (2) The area of triangle ADC is 32. OE To find area of shaded region, you need to find area of triangle ACD, and subtract area of unshaded region inside this triangle from it. To find area of unshaded region, you need to first draw in a line perpendicular to diameter AB of circle from center O to diagonal AC. Call this point E. This point is also one of endpoints of arc AFE. Attachment: ABCD2.png Arc AFE and radii OA and OE bound a sector of circle O: this sector is one quarter of entire area of circle. Now, if you take area of small triangle AEO, and subtract this area from area of sector OAFE, then you have area of unshaded portion of triangle ADC. So, to solve this question, you need to find area of triangle ADC, one quarter of area of circle O, and area of small triangle AEO. To find these three areas, you need radius of circle, or length of one side of square. (1): This is exactly what we need; once we have radius of circle we can find diameter of circle which is same as a side of square and also same as each leg of right triangle ADC. So you can, with this information, solve for different areas necessary, and then solve for area of shaded region. Sufficient. (2): able to find length of height and width (which are equal to each other) of triangle ADC. Let's say that both base and height of triangle ADC = x. 32 = (½)x^2 → x = 8 You have leg lengths (which are equal) of isosceles right triangle ADC; this means that you also have diameter of circle → radius. Sufficient What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O?Actually there is no need for any calculations. From both statements we have everything "fixed", only one case possible where we know everything possible. (1) The radius of the circle with center O is 4 > diameter = side = 8. We have "fixed" circle and square. We can find anything there. Sufficient. (2) The area of triangle ADC is 32 > 1/2*AD^2=32 > AD=8 > AD = diameter = 8. The same info as above. 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 29 Aug 2013
Posts: 12

Re: What is the area of the shaded region above, if ABCD
[#permalink]
Show Tags
11 Jan 2014, 15:55
Bunuel wrote: goodyear2013 wrote: Attachment: ABCD.png What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O? (1) The radius of the circle with center O is 4. (2) The area of triangle ADC is 32. OE To find area of shaded region, you need to find area of triangle ACD, and subtract area of unshaded region inside this triangle from it. To find area of unshaded region, you need to first draw in a line perpendicular to diameter AB of circle from center O to diagonal AC. Call this point E. This point is also one of endpoints of arc AFE. Attachment: ABCD2.png Arc AFE and radii OA and OE bound a sector of circle O: this sector is one quarter of entire area of circle. Now, if you take area of small triangle AEO, and subtract this area from area of sector OAFE, then you have area of unshaded portion of triangle ADC. So, to solve this question, you need to find area of triangle ADC, one quarter of area of circle O, and area of small triangle AEO. To find these three areas, you need radius of circle, or length of one side of square. (1): This is exactly what we need; once we have radius of circle we can find diameter of circle which is same as a side of square and also same as each leg of right triangle ADC. So you can, with this information, solve for different areas necessary, and then solve for area of shaded region. Sufficient. (2): able to find length of height and width (which are equal to each other) of triangle ADC. Let's say that both base and height of triangle ADC = x. 32 = (½)x^2 → x = 8 You have leg lengths (which are equal) of isosceles right triangle ADC; this means that you also have diameter of circle → radius. Sufficient What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O?Actually there is no need for any calculations. From both statements we have everything "fixed", only one case possible where we know everything possible. (1) The radius of the circle with center O is 4 > diameter = side = 8. We have "fixed" circle and square. We can find anything there. Sufficient. (2) The area of triangle ADC is 32 > 1/2*AD^2=32 > AD=8 > AD = diameter = 8. The same info as above. Sufficient. Answer: D. Bunuel, Can you please explain why if you only have the radius you can find anything. How would you get the AF part? I knew that Statement 1 and 2 gave the same information, but couldn't figure out how to find the white portion in TriangleADC Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 50619

Re: What is the area of the shaded region above, if ABCD
[#permalink]
Show Tags
12 Jan 2014, 05:36
b00gigi wrote: Bunuel wrote: goodyear2013 wrote: Attachment: ABCD.png What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O? (1) The radius of the circle with center O is 4. (2) The area of triangle ADC is 32. OE To find area of shaded region, you need to find area of triangle ACD, and subtract area of unshaded region inside this triangle from it. To find area of unshaded region, you need to first draw in a line perpendicular to diameter AB of circle from center O to diagonal AC. Call this point E. This point is also one of endpoints of arc AFE. Attachment: ABCD2.png Arc AFE and radii OA and OE bound a sector of circle O: this sector is one quarter of entire area of circle. Now, if you take area of small triangle AEO, and subtract this area from area of sector OAFE, then you have area of unshaded portion of triangle ADC. So, to solve this question, you need to find area of triangle ADC, one quarter of area of circle O, and area of small triangle AEO. To find these three areas, you need radius of circle, or length of one side of square. (1): This is exactly what we need; once we have radius of circle we can find diameter of circle which is same as a side of square and also same as each leg of right triangle ADC. So you can, with this information, solve for different areas necessary, and then solve for area of shaded region. Sufficient. (2): able to find length of height and width (which are equal to each other) of triangle ADC. Let's say that both base and height of triangle ADC = x. 32 = (½)x^2 → x = 8 You have leg lengths (which are equal) of isosceles right triangle ADC; this means that you also have diameter of circle → radius. Sufficient What is the area of the shaded region above, if ABCD is a square and line segment AB is a diameter of the circle with center O?Actually there is no need for any calculations. From both statements we have everything "fixed", only one case possible where we know everything possible. (1) The radius of the circle with center O is 4 > diameter = side = 8. We have "fixed" circle and square. We can find anything there. Sufficient. (2) The area of triangle ADC is 32 > 1/2*AD^2=32 > AD=8 > AD = diameter = 8. The same info as above. Sufficient. Answer: D. Bunuel, Can you please explain why if you only have the radius you can find anything. How would you get the AF part? I knew that Statement 1 and 2 gave the same information, but couldn't figure out how to find the white portion in TriangleADC Thanks That's the beauty of DS: we don't need to solve if we know that we CAN solve. We can solve because we know the radius of the circle (so we know everything about it) and we know the side of the square (so we know everything about it). If still interested in solving you can check under the spoiler in the initial post.
_________________
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: 03 Oct 2014
Posts: 132
Location: India
Concentration: Operations, Technology
WE: Engineering (Aerospace and Defense)

Re: What is the area of the shaded region above, if ABCD
[#permalink]
Show Tags
27 Jan 2015, 11:42
D
One subtle hint....both the options A and B pointing towards same conclusion.....so can be either D or E....
Like the solution provided in spoiler....either is enough



NonHuman User
Joined: 09 Sep 2013
Posts: 8786

Re: What is the area of the shaded region above, if ABCD
[#permalink]
Show Tags
10 Sep 2018, 19:13
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




Re: What is the area of the shaded region above, if ABCD &nbs
[#permalink]
10 Sep 2018, 19:13






