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

 It is currently 15 Nov 2018, 19:23

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 117
A circular mat with diameter 20 inches is placed on a square  [#permalink]

### Show Tags

26 Aug 2010, 06:34
1
6
00:00

Difficulty:

65% (hard)

Question Stats:

64% (02:08) correct 36% (02:16) wrong based on 494 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
Math Expert
Joined: 02 Sep 2009
Posts: 50613
A circular mat with diameter 20 inches is placed on a square  [#permalink]

### Show Tags

26 Aug 2010, 07:37
7
3
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.

_________________
##### General Discussion
Manager
Joined: 19 Apr 2010
Posts: 177
Schools: ISB, HEC, Said
Re: Closest Fraction Calculation Problem  [#permalink]

### Show Tags

27 Aug 2010, 04:29
Nice explanation Bunuel... Thanks
Manager
Joined: 19 Mar 2012
Posts: 154
Location: United States
Concentration: Finance, General Management
GMAT 1: 750 Q50 V42
GPA: 3.69
WE: Analyst (Mutual Funds and Brokerage)
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: 101
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
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: 50613
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: 29
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.
Board of Directors
Joined: 17 Jul 2014
Posts: 2645
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
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: 101
GMAT 1: 600 Q33 V40
GPA: 3.3
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
Manager
Joined: 03 Jan 2017
Posts: 156
Re: A circular mat with diameter 20 inches is placed on a square  [#permalink]

### Show Tags

12 Mar 2017, 09:44
let's do it in a few steps:
1) area of a mat: 10^2*3,14
2) area of a table: 24*24
then we can arrive at cca 77/144

Let's look at answer choices, they're in ascending order, 1/2 seems fine if tested
Intern
Joined: 23 Aug 2016
Posts: 48
Re: A circular mat with diameter 20 inches is placed on a square  [#permalink]

### Show Tags

08 May 2017, 23:09
Area of the Square = 24*24
Area of the Circle = 3*10*10 (approximating pi as 3)

Fraction of the square covered by the circle = 3*10*10 / 24*24
Cancel the 3 with one 24, reduce the two tens = 25/48, which is roughly 1/2. Answer C
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A circular mat with diameter 20 inches is placed on a square  [#permalink]

### Show Tags

12 May 2017, 12:32
1
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

Since the diameter of the mat is 20 inches, the radius is 10 inches. The area of the mat is:

area = πr^2 = π(10)^2 = 3.14 x 100 = 314 square inches

Since each side of the square tabletop is 24 inches long, the area is:

area = side^2 = 24 x 24 = 576 square inches

Thus, the fraction of the table covered by the mat is 314/576 = 157/288

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Joined: 04 Sep 2015
Posts: 510
Location: India
WE: Information Technology (Computer Software)
Re: A circular mat with diameter 20 inches is placed on a square  [#permalink]

### Show Tags

15 Sep 2018, 12:52
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

so to solve this I worked like...

area of the mat/total area of the square tabletop
3.14*10*10/24*24=
314/576, which is closest to 1/2. so i picked C.
Re: A circular mat with diameter 20 inches is placed on a square &nbs [#permalink] 15 Sep 2018, 12:52
Display posts from previous: Sort by