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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hi:

Someone solved Stolyar's original YIN-YAN problem too quickly so I decided to add a little twist to make it more "interesting."

In the attached diagram, the assumptions are the same as in Stolyar's problem (A, B, C are on diameter, center of circle is B, and all arcs are semicircles). Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded area region above the red line to the area of the shaded region below the red line? (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

Attachments

ying.jpg [ 11.69 KiB | Viewed 1023 times ]

ying.jpg [ 11.69 KiB | Viewed 1027 times ]

_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

Someone solved Stolyar's original YIN-YAN problem too quickly so I decided to add a little twist to make it more "interesting."

In the attached diagram, the assumptions are the same as in Stolyar's problem (A, B, C are on diameter, center of circle is B, and all arcs are semicircles). Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded area region above the red line to the area of the shaded region below the red line? (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

stolyar, what if the info YXA = 105 is not given.

can we still solve the problem.

I tried using the property that an angle inscribed in a semicircle is 90.

So i get AYC = 90 and AXC = 90 . Also ABC,BYC and XYB are

I do not think so.
If an angle is not given, then point Y can slide anywhere around the circle, making parts of the shaded region change. We need to fix point Y somehow.

I do not think so. If an angle is not given, then point Y can slide anywhere around the circle, making parts of the shaded region change. We need to fix point Y somehow.

Stolyar was able to solve this very nicely, but I deleted his post so that everyone else would have a chance to solve it.

P.S.: Stolyar -- everyone knows you are a whiz. Since you are a moderator, please give everyone a chance to solve before solving! (you can always message your solution to me privately and I will let you know how you did and give you credit if you get it right).
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

If angle axy=105 then sector acy=210. obviously sector ac=180 right. Thus, sector yc=30 (210-180). Sector yc is enclosed by the central angle ybc, making angle ycb=30 degrees. 30/360 = 1/12. so the area of that portion is pi/12.

the area of the semi circle is .5*(.5)^2*pi or pi/8

so the area below the red line is pi/12 + pi/8 = 5pi/24

the area of the shaded region is pi/2 (see original ying yang problem).

thus the area above the red line is pi/2 -pi/12 - pi/8 = 7pi/24

the ratio requested in the problem is (7pi/24)/(5pi/24) = 7/5

Great problems akamai. If the teachers at that math work shop are half as good as you then i'm sure i would have gotten my money's worth, too bad they're filled up.
Keep em coming

the problem states that axy = 105. For any non-central angle in a circle the sector enclosed by that angle is always twice that angle. For a central angle the sector is the same as the angle. For example if xby = 80 then sector xy would also equal 80.