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.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
16 Sep 2014, 00:28
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:07) correct
36%
(02:36)
wrong
based on 680
sessions
History
Date
Time
Result
Not Attempted Yet
A circle with a radius \(r\) is inscribed in a square with side \(s\). If the ratio of the area of the square to the area of the circle is \(m\), and the ratio of the perimeter of the square to that of the circle is \(n\), which of the following must be true? (The area of a circle is \(\pi r^2\) and the perimeter of a circle is \(2 \pi r\))
A. \(\frac{m}{n} > 1\)
B. \(\frac{m}{n} = 1\)
C. \(1\gt \frac{m}{n} > \frac{1}{2}\)
D. \(\frac{m}{n} = \frac{1}{2}\)
E. \(\frac{m}{n} < \frac{1}{2}\)
16 Sep 2014, 00:28
Kudos
Bookmarks
Official Solution:
A circle with a radius \(r\) is inscribed in a square with side \(s\). If the ratio of the area of the square to the area of the circle is \(m\), and the ratio of the perimeter of the square to that of the circle is \(n\), which of the following must be true? (The area of a circle is \(\pi r^2\) and the perimeter of a circle is \(2 \pi r\))
A. \(\frac{m}{n} > 1\)
B. \(\frac{m}{n} = 1\)
C. \(1\gt \frac{m}{n} > \frac{1}{2}\)
D. \(\frac{m}{n} = \frac{1}{2}\)
E. \(\frac{m}{n} < \frac{1}{2}\)
Note that this is not a Geometry question. While it uses basic knowledge of figures, it is actually a Ratios question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Using a number-picking approach:
Assume \(s = 6\). For the inscribed circle, \(r = \frac{s}{2} = \frac{6}{2} = 3\). Consequently, the area of the square is \(6 * 6 = 36\) and the area of the circle is \(\pi*r^2 = 9\pi\). The ratio \(m\) is \(\frac{4}{\pi}\).
The perimeter of the square is \(4s=24\) and the perimeter of the circle is \(2\pi r = 6\pi\). The ratio \(n\) is \(\frac{4}{\pi}\).
Therefore, \(m = n\), so \(\frac{m}{n} = 1\).
Algebraic approach:
Using an algebraic approach:
"A circle with a radius \(r\) is inscribed in a square with side \(s\)" implies \(s = 2r\);
"The ratio of the area of the square to the area of the circle is \(m\)" can be written as \(m = \frac{s^2}{\pi{r^2} } = \frac{(2r)^2}{\pi{r^2} }=\frac{4}{\pi}\).
"The ratio of the perimeter of the square to that of the circle is \(n\)" can be stated as \(n = \frac{4s}{2\pi{r} }= \frac{4(2r)} { 2\pi{r} }=\frac{4}{\pi}\).
Therefore, \(m = n\), so \(\frac{m}{n} = 1\).
Answer: B
A circle with a radius \(r\) is inscribed in a square with side \(s\). If the ratio of the area of the square to the area of the circle is \(m\), and the ratio of the perimeter of the square to that of the circle is \(n\), which of the following must be true? (The area of a circle is \(\pi r^2\) and the perimeter of a circle is \(2 \pi r\))
A. \(\frac{m}{n} > 1\)
B. \(\frac{m}{n} = 1\)
C. \(1\gt \frac{m}{n} > \frac{1}{2}\)
D. \(\frac{m}{n} = \frac{1}{2}\)
E. \(\frac{m}{n} < \frac{1}{2}\)
Note that this is not a Geometry question. While it uses basic knowledge of figures, it is actually a Ratios question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Using a number-picking approach:
Assume \(s = 6\). For the inscribed circle, \(r = \frac{s}{2} = \frac{6}{2} = 3\). Consequently, the area of the square is \(6 * 6 = 36\) and the area of the circle is \(\pi*r^2 = 9\pi\). The ratio \(m\) is \(\frac{4}{\pi}\).
The perimeter of the square is \(4s=24\) and the perimeter of the circle is \(2\pi r = 6\pi\). The ratio \(n\) is \(\frac{4}{\pi}\).
Therefore, \(m = n\), so \(\frac{m}{n} = 1\).
Algebraic approach:
Using an algebraic approach:
"A circle with a radius \(r\) is inscribed in a square with side \(s\)" implies \(s = 2r\);
"The ratio of the area of the square to the area of the circle is \(m\)" can be written as \(m = \frac{s^2}{\pi{r^2} } = \frac{(2r)^2}{\pi{r^2} }=\frac{4}{\pi}\).
"The ratio of the perimeter of the square to that of the circle is \(n\)" can be stated as \(n = \frac{4s}{2\pi{r} }= \frac{4(2r)} { 2\pi{r} }=\frac{4}{\pi}\).
Therefore, \(m = n\), so \(\frac{m}{n} = 1\).
Answer: B
General Discussion
23 Nov 2015, 06:08
Kudos
Bookmarks
I understand the logic of the answer but I was a bit confused by the question. I imagined that the circle could have been any size that would fit within the confines of the square, so that the relationship between R and K was not clear (the picture I had was of a small circle etched onto the side of a wooden block).
When a question states that a shape is 'inscribed' into another, should we always understand this as meaning that the new shape exactly touches the edge of the older shape?
When a question states that a shape is 'inscribed' into another, should we always understand this as meaning that the new shape exactly touches the edge of the older shape?
