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:

A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

I. 0.01

II. 2.00

III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Look at the diagram below:

If the width of blue rectangle is small enough then its area could be 0.01.

Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle).

Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible)

After reading this explanation, I came up with this doubt: If we draw the diagonals of the rectangle (the blue region), each of the diagonals would pass through the center which- would be same as the diameter of the circle. Right or wrong? I am not able to prove this wrong.

After reading this explanation, I came up with this doubt: If we draw the diagonals of the rectangle (the blue region), each of the diagonals would pass through the center which- would be same as the diameter of the circle. Right or wrong? I am not able to prove this wrong.

Right. A rectangle has right angles. A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle). The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled (right angel being the angle opposite the diameter/hypotenuse)
_________________

Then should the area of the rectangle be 1/2*d1*d2= 1/2*2*2=2?. I think I am getting this wrong, but where I don't know.

If the rectangle is a square then the area would be 2 (as given in the solution). Don't understand what you derive from this and what's your doubt.
_________________

This is a great question. Very enlightening. There is a question about a small ''technicallity'' though.

The question stem asks about a ''rectangle''. Since the area of 2 is only achieved throught a square isn't it provoking a little doubt that you could marginally discard the area =2 because ''technically'' the questions asks about rectangle ?

This is a great question. Very enlightening. There is a question about a small ''technicallity'' though.

The question stem asks about a ''rectangle''. Since the area of 2 is only achieved throught a square isn't it provoking a little doubt that you could marginally discard the area =2 because ''technically'' the questions asks about rectangle ?

I hope my question is not awkwardly written

_____________________ All squares are rectangles.
_________________

A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

I. 0.01

II. 2.00

III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Look at the diagram below:

If the width of blue rectangle is small enough then its area could be 0.01.

Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle).

Now,since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible)

Answer: D

Hello Bunuel i have a question for the highlighted area - shouldn't the max area of square inscribed within a circle with diameter of 2 be 2*pi? let a = side of square... diameter = diagonal 2 = a*sqrt(2) a = sqrt(2). Area = pi*a^2 = 2*pi. So => 0 <= area < 2*pi Please let me know if i am missing something!!!

A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

I. 0.01

II. 2.00

III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Look at the diagram below:

If the width of blue rectangle is small enough then its area could be 0.01.

Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle).

Now,since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible)

Answer: D

Hello Bunuel i have a question for the highlighted area - shouldn't the max area of square inscribed within a circle with diameter of 2 be 2*pi? let a = side of square... diameter = diagonal 2 = a*sqrt(2) a = sqrt(2). Area = pi*a^2 = 2*pi. So => 0 <= area < 2*pi Please let me know if i am missing something!!!

Not sure what you are doing there. If a square is inscribed in a circle with the diameter of 2, then the area of the square would simply be diagonal^2/2 = 4/2 = 2 (because diameter=diagonal).
_________________

A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

I. 0.01

II. 2.00

III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Look at the diagram below:

If the width of blue rectangle is small enough then its area could be 0.01.

Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle).

Now,since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible)

Answer: D

Hello Bunuel i have a question for the highlighted area - shouldn't the max area of square inscribed within a circle with diameter of 2 be 2*pi? let a = side of square... diameter = diagonal 2 = a*sqrt(2) a = sqrt(2). Area = pi*a^2 = 2*pi. So => 0 <= area < 2*pi Please let me know if i am missing something!!!

Not sure what you are doing there. If a square is inscribed in a circle with the diameter of 2, then the area of the square would simply be diagonal^2/2 = 4/2 = 2 (because diameter=diagonal).

Hello Bunuel I got my mistake - we are talking about largest rectangle (square) within a circle - thus area of square - a^2 => 2. My bad.