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:

Q109. In triangle ABC, pt. X is the midpt. of side AC and [#permalink]

Show Tags

01 Jul 2009, 11:13

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

100% (01:39) correct
0% (00:00) wrong based on 29 sessions

HideShow timer Statistics

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

Q109. In triangle ABC, pt. X is the midpt. of side AC and pt. Y is the midpt. of side BC. If pt. R is the midpt. of line segment XC and if pt. S is the midpt. of the line segment YC, what is the area of trianglular region RCS?

1) Area of triangle region ABX is 32 2) The length of one of the altitudes of triangle ABC is 8.

it should be in math forum... but my guess is A - 1) is sufficient...

Sure you dont know the B/H to form the area of 32 but the area of the triangle RCS uses the same basic Base and Height (BXH), just in a very smaller ratio to the original area. I think there is a triangle ratio rule or something that you can use from the knowledge of the midpoints.... it's been a while
_________________

When you have 1 midpoint and draw it to the opposing vertex you get a 1:2 ratio of the original area. Now you do that with 3 midpoints in the beginning you should get 6 equal pieces. Now you have the last 2 midpoints which is splitting the 1/3 of the total area apart into 6 pieces. you want 2 of the 6 pieces for the area.
_________________

1) A line connecting midpoint of any side and the opposite vertex will divide the triangle in 2 halves equal in area 2) If a line connects midpoints of any two sides, then the smaller triangle thus formed will be proportional to the area of the original triangle in area. ie area of larger : area of smaller triangle = 4:1

Now connect XB. area AXB = area BXC = 16

connect XY, (applying rule 1 again for BXC) area BYX = area CYX = 8