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:

60% (01:19) correct
40% (01:25) wrong based on 211 sessions

HideShow timer Statistics

A circle is inscribed right in the middle of a semicircle with a diameter of \(\pi\) as shown below. What is the ratio of the area of the semicircle to the area not covered by the inscribed circle?

A circle is inscribed right in the middle of a semicircle with a diameter of \(\pi\) as shown below. What is the ratio of the area of the semicircle to the area not covered by the inscribed circle?

A. 4:1 B. 3:2 C. 3:1 D. 4:3 E. 2:1

Since the radius of the big circle (\(\frac{\pi}{2}\)) is twice the radius of the inscribed circle (\(\frac{\pi}{4}\)) then its area is 4 times greater than the area of the inscribed circle (because in the area formula the radius is squared. For example the area of a circle with radius of 2 is \(4\pi\), which is 4 times greater than the radius of a circle with the radius of 1, which is \(\pi\)).

Thus the area of the semicircle is \(\frac{4}{2}=2\) times greater than the area of the inscribed circle: so, the area of the semicircle is 2 units, the area of the inscribed circle is 1 unit, and the area of the semicircle not covered by the inscribed circle is also 1 unit. Ratio: \(\frac{2}{1}\).

A circle is inscribed right in the middle of a semicircle with a diameter of \(\pi\) as shown below. What is the ratio of the area of the semicircle to the area not covered by the inscribed circle?

A. 4:1 B. 3:2 C. 3:1 D. 4:3 E. 2:1

hi.. ans E... it can be found just by looking at the figure .. As ratio of the areas would just depend on square of the radius.. we get area of the outer circle to be 4 times of smaller circle as radius of smaller is half of that of larger circle. So the ratio will come down to 2:1 as we are comparing half of outer circle with full inner circle
_________________

A circle is inscribed right in the middle of a semicircle with a diameter of \(\pi\) as shown below. What is the ratio of the area of the semicircle to the area not covered by the inscribed circle?

A. 4:1 B. 3:2 C. 3:1 D. 4:3 E. 2:1

As Randude has already mentioned, the question is a good one but missing the "pi" in the figure. Admin, please correct the figure. Thank you.

Thus the area of the semicircle is \(\frac{4}{2}=2\) times greater than the area of the inscribed circle: so, the area of the semicircle is 2 units, the area of the inscribed circle is 1 unit, and the area of the semicircle not covered by the inscribed circle is also 1 unit. Ratio: \(\frac{2}{1}\).

Answer: E

why is the area of the semicircle NOT covered by the inscribed circle also 1?!
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Thus the area of the semicircle is \(\frac{4}{2}=2\) times greater than the area of the inscribed circle: so, the area of the semicircle is 2 units, the area of the inscribed circle is 1 unit, and the area of the semicircle not covered by the inscribed circle is also 1 unit. Ratio: \(\frac{2}{1}\).

Answer: E

why is the area of the semicircle NOT covered by the inscribed circle also 1?!

If the area of the semicircle is 2 and the area of the inscribed circle is 1, then how much is the area of the semicircle not covered by the inscribed circle? 2 - 1 = 1.
_________________

I think this is a high-quality question and I don't agree with the explanation. The explanation states that the area of the circle with bigger radius is four times 'greater' than that with the smaller radius. I think it should be four times and not four times 'greater' as that would affect the answer.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. How do we know the that the radius of smaller circle is half of the semicircle?

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. How do we know the that the radius of smaller circle is half of the semicircle?

Small circle is centered in the semicircle, thus diameter of smaller circle is equal to the radius of the semicircle.
_________________

But the question says "What is the ratio of the area of the semicircle to the area not covered by the inscribed circle?" so answer should be 4:3

The answer should be and is 2:1. Please check the discussion above and post your own solution to help you in finding where you went wrong there.
_________________