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

 It is currently 26 Aug 2019, 02:49

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

Is the area of circle C greater than the area of square S?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57298
Is the area of circle C greater than the area of square S?  [#permalink]

Show Tags

21 May 2016, 03:50
1
2
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:06) correct 42% (01:58) wrong based on 117 sessions

HideShow timer Statistics

Is the area of circle C greater than the area of square S?

(1) The diameter of C is equal to the diagonal of square S.
(2) The perimeter of S is less than the circumference of C.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7754
Is the area of circle C greater than the area of square S?  [#permalink]

Show Tags

21 May 2016, 05:13
2
Bunuel wrote:
Is the area of circle C greater than the area of square S?

(1) The diameter of C is equal to the diagonal of square S.
(2) The perimeter of S is less than the circumference of C.

Hi,
Area of a circle is dependent on radius, r, and That of square on side, say a..
so if we know the ratio between radius and the side we can answer the Q..

(1) The diameter of C is equal to the diagonal of square S.
This tells us that $$2r=\sqrt{2}a$$..
Suff..

(2) The perimeter of S is less than the circumference of C.
since we are dealing with inequality sign, always better to check for the values..
$$4a<2*pi*r................. a<pi*\frac{r}{2}$$.....................
since both sides are +ive, square both sides...
$$a^2<(pi*\frac{r}{2})^2.........................a^2<pi*r^2*\frac{pi}{4}$$.......................
since pi/4 <1, we can safely say $$a^2<pi*r^2$$ OR area of square < area of circle
Suff

D
_________________
Senior Manager
Joined: 19 Oct 2012
Posts: 273
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)
Is the area of circle C greater than the area of square S?  [#permalink]

Show Tags

27 Sep 2017, 19:37
We need to find if Area(C) >Area(S)

Let the side of the square is 'a' and radius of the circle be 'r'.

Stmt1: diameter (d)=$$\sqrt{2}a$$
on solving this we get, radius r = $$\sqrt{2}a/2$$
Using this relation we can deduce a relationship between the areas, hence we don't need to solve any further. This statement is sufficient.

Stmt2: $$4a<2 * pi * r$$
=> $$2a<pi*r$$
On squaring both sides...
=> $$a^2 < (pi^2 * r^2)/4$$

Again a clear relationship between a and r can be found here.. Hence this statement is sufficient.

_________________
Citius, Altius, Fortius
Non-Human User
Joined: 09 Sep 2013
Posts: 12097
Re: Is the area of circle C greater than the area of square S?  [#permalink]

Show Tags

08 Aug 2019, 18:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is the area of circle C greater than the area of square S?   [#permalink] 08 Aug 2019, 18:54
Display posts from previous: Sort by