Last visit was: 27 Apr 2026, 07:53 It is currently 27 Apr 2026, 07:53
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
sludge
User avatar
Joined: 23 Dec 2006
Last visit: 16 Mar 2013
Posts: 49
Own Kudos:
55
Posts: 49
Kudos: 55
In the diagram to the right, points A, B, and C are on the 18 Sep 2007, 17:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

History

Date
Time
Result
Not Attempted Yet
In the diagram to the right, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the red line to the area of the shaded region below the red line? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

(A) 3/4
(B) 5/6
(C) 1
(D) 7/5
(E) 9/7









best i can figure out is it works out to (.75pi + x)/(1.25pi - x) where x represents the amount of space between the red line and a line at a right angle (on the left) of line AC. but ive got no clue how to find out what x is.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
bkk145
User avatar
Joined: 10 Jun 2007
Last visit: 23 Feb 2014
Posts: 645
Own Kudos:
1,801
Posts: 645
Kudos: 1,801
In the diagram to the right, points A, B, and C are on the 18 Sep 2007, 21:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sludge
In the diagram to the right, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the red line to the area of the shaded region below the red line? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

(A) 3/4
(B) 5/6
(C) 1
(D) 7/5
(E) 9/7









best i can figure out is it works out to (.75pi + x)/(1.25pi - x) where x represents the amount of space between the red line and a line at a right angle (on the left) of line AC. but ive got no clue how to find out what x is.
Show more


Very tough problem, but end up with D.

First, just imagine the same circle without the ying/yang stuff. Connect all the points so that you can end up with three isosceles triangles of ABX, XBY, and YBC. What we want to find is the angle YBC and ABY.

Set angle ABX = x
angle XBY = y
angle YBC = z

We know two equations from here:
(1) x+y+z = 180
Now, knowing that YXA = 105, we can use the isosceles triangle properties to get this equation:
(2) (180-x)/2 + (180-y)/2 = 105

From (2), we get
180 - x + 180 - y = 210
=> x+y = 360 - 210 = 150

Substitute this in (1), you get
150 + z = 180
z = 30

Now we know that angle YBC=30 and ABY = 150

To get the answer, you must find the ratio of the areas. If Ac = area of the big circle and As = area of the semi circle, this ratio will give you the answer:

Ans = [(150/360)*Ac - As] / [(30/360)*Ac +As]

What is missing here is the relationship between Ac and As. Knowing that half of the big circle radius is the radius of the semi circle, we can set the following:

(3) Ac = pai*r^2
(4) As = (pai*(r/2)^2)/2

From (3), you get
r^2 = Ac/pai
Plug in (4), you get
As = pai*(Ac/pai) / 8 = Ac/8

Ans = [(150/360)*Ac - (Ac/8)] / [(30/360)*Ac +(Ac/8)]
= [(150/360) - (1/8)] / [(30/360) +(1/8)]
= 7/5
User avatar
beckee529
User avatar
Joined: 11 Jun 2007
Last visit: 23 Feb 2012
Posts: 393
Own Kudos:
1,976
Posts: 393
Kudos: 1,976
In the diagram to the right, points A, B, and C are on the 18 Sep 2007, 23:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bkk145
sludge
In the diagram to the right, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the red line to the area of the shaded region below the red line? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

(A) 3/4
(B) 5/6
(C) 1
(D) 7/5
(E) 9/7









best i can figure out is it works out to (.75pi + x)/(1.25pi - x) where x represents the amount of space between the red line and a line at a right angle (on the left) of line AC. but ive got no clue how to find out what x is.

Very tough problem, but end up with D.

First, just imagine the same circle without the ying/yang stuff. Connect all the points so that you can end up with three isosceles triangles of ABX, XBY, and YBC. What we want to find is the angle YBC and ABY.

Set angle ABX = x
angle XBY = y
angle YBC = z

We know two equations from here:
(1) x+y+z = 180
Now, knowing that YXA = 105, we can use the isosceles triangle properties to get this equation:
(2) (180-x)/2 + (180-y)/2 = 105

From (2), we get
180 - x + 180 - y = 210
=> x+y = 360 - 210 = 150

Substitute this in (1), you get
150 + z = 180
z = 30

Now we know that angle YBC=30 and ABY = 150

To get the answer, you must find the ratio of the areas. If Ac = area of the big circle and As = area of the semi circle, this ratio will give you the answer:

Ans = [(150/360)*Ac - As] / [(30/360)*Ac +As]

What is missing here is the relationship between Ac and As. Knowing that half of the big circle radius is the radius of the semi circle, we can set the following:

(3) Ac = pai*r^2
(4) As = (pai*(r/2)^2)/2

From (3), you get
r^2 = Ac/pai
Plug in (4), you get
As = pai*(Ac/pai) / 8 = Ac/8

Ans = [(150/360)*Ac - (Ac/8)] / [(30/360)*Ac +(Ac/8)]
= [(150/360) - (1/8)] / [(30/360) +(1/8)]
= 7/5
Show more


holy crap! how long did it take you to figure out the problem and arrive at the solution? very good explanation... you're likely to get 51 for quant!
User avatar
ashkrs
User avatar
Joined: 08 Jun 2007
Last visit: 21 Feb 2019
Posts: 282
Own Kudos:
345
GMAT 1: 680 Q48 V35
Posts: 282
Kudos: 345
In the diagram to the right, points A, B, and C are on the 19 Sep 2007, 08:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sludge
In the diagram to the right, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the red line to the area of the shaded region below the red line? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

(A) 3/4
(B) 5/6
(C) 1
(D) 7/5
(E) 9/7




best i can figure out is it works out to (.75pi + x)/(1.25pi - x) where x represents the amount of space between the red line and a line at a right angle (on the left) of line AC. but ive got no clue how to find out what x is.
Show more



Minutes to gaze into the diagram - 10
Minutes to put down the solution - 2
Feeling after solving the problem - priceless

I am surely going to skip this question in actual test if I am not able to solve in 5 mins.

Here how I arrive at D
Basically what we just need is angle YBA and after that its cake walk.

ratio reqd is (YBA/360 - 1/8) / (YBC/360 +1/8 )

Assume YXB = x and AXB = y
x+y = 105
So XYB is also x and XAB = y because of isoscleles nature.

So YBA becomes 180 -2x + 180 - 2y = 360-2(x+y)
Substituting x+y we get YBA = 360 - 2*105 = 360 -210 = 150 . So YBC=30

Put the values in the ration equation

150/360 - 1/8
30/360 + 1/8

which gives 7/5
User avatar
bkk145
User avatar
Joined: 10 Jun 2007
Last visit: 23 Feb 2014
Posts: 645
Own Kudos:
1,801
Posts: 645
Kudos: 1,801
In the diagram to the right, points A, B, and C are on the 19 Sep 2007, 10:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
beckee529 Thanks for that...
It took at least 5mins to solve this question. However, if this were on the test, you can guess that it is either D or E.
A,B,C doesn't make any sense.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
109928 posts