Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
10 Aug 2022, 01:30
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (03:17) correct
41%
(02:57)
wrong
based on 41
sessions
History
Date
Time
Result
Not Attempted Yet
In the following figure, AB is the diameter of semicircle with center M. Two semi-circles are drawn with AM and MB as the diameters. A circle is drawn such that it is tangent to all the three semi-circles. If AM = \(r\) units, find the radius of the circle (in terms of \(r\)).
A) \(\frac{r}{2}\)
B) \(\frac{r}{3}\)
C) \(\frac{r}{4}\)
D) \(\frac{r}{{\sqrt{2}}}\)
E) \(\frac{2r}{5}\)
1.png [ 8.92 KiB | Viewed 2445 times ]
Are You Up For the Challenge: 700 Level Questions
A) \(\frac{r}{2}\)
B) \(\frac{r}{3}\)
C) \(\frac{r}{4}\)
D) \(\frac{r}{{\sqrt{2}}}\)
E) \(\frac{2r}{5}\)
Attachment:
1.png [ 8.92 KiB | Viewed 2445 times ]
Are You Up For the Challenge: 700 Level Questions
10 Aug 2022, 07:58
Kudos
Bookmarks
Bunuel
We can start by drawing in the red triangle.
Rather than working with the variable r, let's assign a value that we can then plug in to the answer choices. r=2 looks like it will work well since it makes the base of the red triangle equal to 1. So, r=2.
Now, the base of the red triangle is 1, the height is 2-x, and the hypotenuse is 1+x. We can plug those into the Pythagorean theorem.
\(1^2+(2-x)^2=(1+x)^2\)
\(1+4-4x+x^2 = 1+2x+x^2\)
\(4=6x\)
\(x=\frac{2}{3}\)
Let's plug r=2 into the answer choices to find which results in \(\frac{2}{3}\).
A) \(\frac{2}{2}\)
Nope.
B) \(\frac{2}{3}\)
Yep!
Answer choice B.
Attachments
Picture2.png [ 232.51 KiB | Viewed 2094 times ]
Moderator:
