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

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

by mitzwillrockgmat » Sat Jun 12, 2010 8:09 am
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

I would like to know alternate approaches to this problem. I had trouble with this question when doing it under time restrictions. I got so annoyed with it coz it seems so simple that i spent 10 mins on it & still got it wrong! :(

However, under no constraints i eventually figured it out. What I am interested in knowing is how should i approach such problems?

This is how i eventually figured it out....

need to find mat area/table area so pie*10^2/24^2 = 314/576

i realised after dividing numerator and denominator by 2 that i wasn't going to be able to simplify further as 157 is prime (which took me another min or so to figure out!)

so i just decided to see if the fraction is greater than or less than half.

314/576 is a little greater than 1/2. so based on this i can cancel all answers <1/2

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

but both d & e are much greater than half so i selected C eventually.

Is this approach ok?? Does anybody know another way to do this question?

Also, if anyone knows a quick method to identify a prime no. please let me know! Thanks :))))
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by kstv » Sat Jun 12, 2010 8:22 am
TTr²/24² = (22/7) * 10*10/24*24
22/7 is very close to 21/7 = slightly more then 3
so 10*10/8*24
again 24*8 is very close to 25*8
or slightly less than 200
the approximation made in the numerator 22/7 will balance out
the approximation in the denominator
left with 10*10/200 = 1/2
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by Stuart@KaplanGMAT » Sat Jun 12, 2010 12:34 pm
mitzwillrockgmat 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

I would like to know alternate approaches to this problem. I had trouble with this question when doing it under time restrictions. I got so annoyed with it coz it seems so simple that i spent 10 mins on it & still got it wrong! :(

However, under no constraints i eventually figured it out. What I am interested in knowing is how should i approach such problems?

This is how i eventually figured it out....

need to find mat area/table area so pie*10^2/24^2 = 314/576

i realised after dividing numerator and denominator by 2 that i wasn't going to be able to simplify further as 157 is prime (which took me another min or so to figure out!)

so i just decided to see if the fraction is greater than or less than half.

314/576 is a little greater than 1/2. so based on this i can cancel all answers <1/2

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

but both d & e are much greater than half so i selected C eventually.

Is this approach ok?? Does anybody know another way to do this question?

Also, if anyone knows a quick method to identify a prime no. please let me know! Thanks :))))
Great job narrowing it down to D and E; now let's use our denominator to choose the right answer.

1/2 = 288/576
3/4 = 432/576
5/6 = way too much

our answer: 314/576

Well, 314 is closer to 288 than to 432; accordingly, 1/2 is the closest fraction among the answers: choose (C).
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by mitzwillrockgmat » Sat Jun 12, 2010 12:45 pm
Stuart Kovinsky wrote:
mitzwillrockgmat 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

I would like to know alternate approaches to this problem. I had trouble with this question when doing it under time restrictions. I got so annoyed with it coz it seems so simple that i spent 10 mins on it & still got it wrong! :(

However, under no constraints i eventually figured it out. What I am interested in knowing is how should i approach such problems?

This is how i eventually figured it out....

need to find mat area/table area so pie*10^2/24^2 = 314/576

i realised after dividing numerator and denominator by 2 that i wasn't going to be able to simplify further as 157 is prime (which took me another min or so to figure out!)

so i just decided to see if the fraction is greater than or less than half.

314/576 is a little greater than 1/2. so based on this i can cancel all answers <1/2

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

but both d & e are much greater than half so i selected C eventually.

Is this approach ok?? Does anybody know another way to do this question?

Also, if anyone knows a quick method to identify a prime no. please let me know! Thanks :))))
Great job narrowing it down to D and E; now let's use our denominator to choose the right answer.

1/2 = 288/576
3/4 = 432/576
5/6 = way too much

our answer: 314/576

Well, 314 is closer to 288 than to 432; accordingly, 1/2 is the closest fraction among the answers: choose (C).

Thanks! That makes the solution foolproof! :)

I was wondering if you could also shed some light on my other question to...how to determine if a number is prime? what is the quickest way of doing so?

this is the method i use:

to see if 157 is prime

find the closest perfect square to this number...that would be 169. 169 is the square of 13.

now divide 157 by all primes less than 13 i.e by 11, 7, 5, 3 & 2

if the no. is not divisible by any of these then the no. is prime.
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by Stuart@KaplanGMAT » Sat Jun 12, 2010 7:15 pm
mitzwillrockgmat wrote:
I was wondering if you could also shed some light on my other question to...how to determine if a number is prime? what is the quickest way of doing so?

this is the method i use:

to see if 157 is prime

find the closest perfect square to this number...that would be 169. 169 is the square of 13.

now divide 157 by all primes less than 13 i.e by 11, 7, 5, 3 & 2

if the no. is not divisible by any of these then the no. is prime.
Your method is as good as any - mathematicians have devoted their entire lives trying to figure out primes and haven't come up with any simple solutions.
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by outreach » Sun Jun 13, 2010 1:27 am
(pi*r^2)/s^2

(22*10*10)/(7*24*24)
(11*5*5)/(7*6*12)
now 11/12 gives approx 0.9
5/7 gives approx 0.7
5/6 gives approx 0.8

0.9*0.7*0.8=0.504

hence the answer should be C
mitzwillrockgmat 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

I would like to know alternate approaches to this problem. I had trouble with this question when doing it under time restrictions. I got so annoyed with it coz it seems so simple that i spent 10 mins on it & still got it wrong! :(

However, under no constraints i eventually figured it out. What I am interested in knowing is how should i approach such problems?

This is how i eventually figured it out....

need to find mat area/table area so pie*10^2/24^2 = 314/576

i realised after dividing numerator and denominator by 2 that i wasn't going to be able to simplify further as 157 is prime (which took me another min or so to figure out!)

so i just decided to see if the fraction is greater than or less than half.

314/576 is a little greater than 1/2. so based on this i can cancel all answers <1/2

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

but both d & e are much greater than half so i selected C eventually.

Is this approach ok?? Does anybody know another way to do this question?

Also, if anyone knows a quick method to identify a prime no. please let me know! Thanks :))))
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