GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 18:05

### 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

we will pick new questions that match your level based on your Timer History

Track

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

# In the figure above, the circle is inscribed in a square that has an a

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335
In the figure above, the circle is inscribed in a square that has an a  [#permalink]

### Show Tags

11 Oct 2018, 03:01
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:01) correct 13% (01:36) wrong based on 52 sessions

### HideShow timer Statistics

In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

(A) $$\frac{25\pi}{4}$$

(B) $$\frac{25\pi}{2}$$

(C) $$25\pi$$

(D) $$50\pi$$

(E) $$\frac{625\pi}{16}$$

Attachment:

Capture (3).JPG [ 12.52 KiB | Viewed 600 times ]

_________________
VP
Joined: 31 Oct 2013
Posts: 1475
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

### Show Tags

11 Oct 2018, 03:06
Bunuel wrote:

In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

(A) $$\frac{25\pi}{4}$$

(B) $$\frac{25\pi}{2}$$

(C) $$25\pi$$

(D) $$50\pi$$

(E) $$\frac{625\pi}{16}$$

Attachment:
Capture (3).JPG

Area of the square = s^2 = 50 = $$5\sqrt{2}$$

Area of the circle = ($$5\sqrt{2}$$/2)^2 pie = 25 / 2 pie.

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4753
Location: India
GPA: 3.5
Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

### Show Tags

11 Oct 2018, 08:52
selim wrote:
Bunuel wrote:

In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

(A) $$\frac{25\pi}{4}$$

(B) $$\frac{25\pi}{2}$$

(C) $$25\pi$$

(D) $$50\pi$$

(E) $$\frac{625\pi}{16}$$

Attachment:
Capture (3).JPG

Area of the square = s^2 = 50 = $$5\sqrt{2}$$

Area of the circle = ($$5\sqrt{2}$$/2)^2 pie = 25 / 2 pie.

+1 for (B), well explained....
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Joined: 13 Jun 2012
Posts: 199
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

### Show Tags

11 Oct 2018, 09:30
Bunuel wrote:

In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

(A) $$\frac{25\pi}{4}$$

(B) $$\frac{25\pi}{2}$$

(C) $$25\pi$$

(D) $$50\pi$$

(E) $$\frac{625\pi}{16}$$

Attachment:
Capture (3).JPG

The Diameter of the circle is the one of the sides of the square.

S^2 (area of the square)= 50 or s=5√2

Area of the circle is πr^2

π* (5√2/2)^2= 25π/2 (B)
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8030
Location: United States (CA)
Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

### Show Tags

13 Oct 2018, 18:47
Bunuel wrote:

In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

(A) $$\frac{25\pi}{4}$$

(B) $$\frac{25\pi}{2}$$

(C) $$25\pi$$

(D) $$50\pi$$

(E) $$\frac{625\pi}{16}$$

Attachment:
Capture (3).JPG

So the area of the circle is:

(√50/2)^2 x π = 50π/4 = 25π/2

Alternate solution:

We can see that area of the inscribed circle is obviously less than the area of the circumscribed square (50) but more than half the area of the square (25). Since we know π is approximately 3.14, of the answer choices, choices C, D and E are too big since each of them is more than 50. Choice A is too small since it’s less than 25. So the correct answer is choice B (and it is between 25 and 50).

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In the figure above, the circle is inscribed in a square that has an a   [#permalink] 13 Oct 2018, 18:47
Display posts from previous: Sort by