A circular mat with diameter 20 inches is placed on a square : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 10 Dec 2016, 09:23

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A circular mat with diameter 20 inches is placed on a square

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 143
Followers: 3

Kudos [?]: 637 [1] , given: 15

A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

26 Aug 2010, 06:34
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:32) correct 38% (01:40) wrong based on 286 sessions

### HideShow timer Statistics

A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6863

Kudos [?]: 90114 [4] , given: 10417

A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

26 Aug 2010, 07:37
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
udaymathapati wrote:
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose
sides is 24 inches long. Which of the following is closest to the fraction of the tabletop
covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6

$$area_{circle}=\pi{r^2}=\pi{10^2}\approx{314}$$ ($$d=20$$ --> $$r=10$$);

$$area_{square}=24^2=576$$;

$$\frac{area_{circle}}{area_{square}}=\frac{314}{576}=\frac{157}{288}$$.

Now this fraction is obviously between 1/2 and 3/4 --> $$\frac{1}{2}=\frac{144}{288}$$ and $$\frac{3}{4}=\frac{216}{288}$$ --> 157 is closer to 144 than to 216.

_________________
Manager
Joined: 19 Apr 2010
Posts: 210
Schools: ISB, HEC, Said
Followers: 4

Kudos [?]: 75 [0], given: 28

Re: Closest Fraction Calculation Problem [#permalink]

### Show Tags

27 Aug 2010, 04:29
Nice explanation Bunuel... Thanks
Manager
Joined: 19 Mar 2012
Posts: 174
Location: United States
Concentration: Finance, General Management
GMAT 1: 750 Q50 V42
GPA: 3.69
WE: Analyst (Mutual Funds and Brokerage)
Followers: 7

Kudos [?]: 46 [0], given: 13

Re: GWD #1 Math 7 [#permalink]

### Show Tags

05 Apr 2012, 11:49
SO we are looking for the area of the cloth over the area of the table

Area of the Cloth = (pi)(r)^2 which is about (3)(10)(10)

Area of the Table = (24)(24)

So the quick way to estimate is looking at the fraction like this: (3/24)(100/24)

I hope this is easy to follow, so with some simplification i get (1/8)(4) = (1/2) Answer is C
Manager
Joined: 26 Feb 2012
Posts: 116
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Followers: 0

Kudos [?]: 19 [0], given: 56

Re: A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

04 May 2013, 03:07
Hi Bunel
Please let me clarify how did you establish 1/2=144/288 and 1/3= 216/288???

Rgds
Prasannajeet
Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6863

Kudos [?]: 90114 [0], given: 10417

Re: A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

04 May 2013, 03:31
prasannajeet wrote:
Hi Bunel
Please let me clarify how did you establish 1/2=144/288 and 1/3= 216/288???

Rgds
Prasannajeet

To compare 157/288, 1/2 ans 1/3 find their common denominator, which is 288 --> 1/2=144/288 (multiply by 144) and 1/3= 216/288 (multiply by 216).
_________________
Intern
Joined: 09 Jun 2012
Posts: 31
Followers: 0

Kudos [?]: 18 [0], given: 13

Re: A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

29 Jul 2013, 01:25
udaymathapati wrote:
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6

Simplified the numbers as below:
Req fraction is (3.14 * 10 * 10)/(24 * 24)
Cancel 10 and 24 by 2: (3.14 * 5 * 5)/(12 * 12)
Cancel 5*5=25 in numerator with 12 in denominator: (3.14 * 2.something)/(1 * 12) = 6.something / 12 =~1/2. (Here it is important to note that 2.something and 6.something are in the lower end, i.e., much lesser than 2.5 and 6.5.)
Bunuel has given a standard way to deal with fraction comparison in the previous posts. In some cases, the above sort of simplifications might help in getting a fraction with realtively smaller numerator and denominators.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12906
Followers: 563

Kudos [?]: 158 [0], given: 0

Re: A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

25 Feb 2015, 21:35
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.
_________________
SVP
Joined: 17 Jul 2014
Posts: 2091
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
WE: General Management (Transportation)
Followers: 18

Kudos [?]: 248 [0], given: 124

Re: A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

04 Nov 2015, 13:41
if D = 20, then r = 10, and area of the circle is 100 pi (I converted pi to 22/7) and thus the area is 2200/7
area of the square is 24^2 = 576
now, to find the area that is covered by the circle, divide 2200/7 by 576. get 2200/4032, which is slightly more than 1/2.

other method, 2200/7 is slightly more than 300
300+/576 = aprox 1/2
Manager
Joined: 05 Jul 2015
Posts: 110
GMAT 1: 600 Q33 V40
GPA: 3.3
Followers: 0

Kudos [?]: 20 [0], given: 3

A circular mat with diameter 20 inches is placed on a square [#permalink]

### Show Tags

21 Nov 2015, 19:42
I don't get why everyone is over-complicating the math here since the question stem clearly asks to ESTIMATE.

Making pi = 3

Area of circle = 2*5*2*5*3
Area of sqr = 12*3*2*2

3s cancel. 4s cancel. left with 25/48 close to 25/50 = 1/2
A circular mat with diameter 20 inches is placed on a square   [#permalink] 21 Nov 2015, 19:42
Similar topics Replies Last post
Similar
Topics:
If 20 circular pepperoni slices each with a 1 inch-diameter cover a ci 1 08 Sep 2016, 18:11
A circular cloth with a diameter of 20 inches is placed on a 1 02 Nov 2013, 04:54
A circular rim A having a diameter of 28 inches is rotating 3 16 Aug 2013, 08:50
4 A circular rim 28 inches in diameter rotates the same number of inches 4 30 Sep 2010, 19:38
8 A circular mat with diameter 20 inches is placed on a square 5 19 Nov 2007, 18:03
Display posts from previous: Sort by