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Questions from Gmatprep2 [#permalink] New post 22 May 2008, 16:15
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If you know how to solve the following problems, please explain your answer.


1) What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?

The correct answer is 1/2

--------------------------------------------------------------------
2) Is 1/p > (r / ((r^2) + 2)?

1) p = r
2) r>0

The correct answer is C.

But I got A:
Here what I did:
1/p > (r / ((r^2) + 2) => pr > r^2 + 2
1) If p = r then r^2 > r^2 + 2

-----------------------------------------------------------------------------------------
3) From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?

The correct answer is 432.
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Director
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Re: Questions from Gmatprep2 [#permalink] New post 22 May 2008, 17:20
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1) What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
a = b = 1, Also, c < a+b, and c> a-b (from properties of triangle)
Also, r =1. (radius of circle)
So min(c) = 0 and max(c) = 2

Now I googled and found that for a circumscribed triangle,
K = abc / 4r { K is the area of triangle, r is radius of circle }

K will be maximum when c is maximum, because, a,b and r are constant and equal to 1.
K = 1*1*2 / 4*1
K = 1/2.
http://courses.ncssm.edu/goebel/STATECO ... RIANGL.htm
Director
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Re: Questions from Gmatprep2 [#permalink] New post 22 May 2008, 17:28
2) Is 1/p > (r / ((r^2) + 2)?
1) p = r
2) r>0
---------------
This is a classic trap of GMAT.
But I got A:
Here what I did:
1/p > (r / ((r^2) + 2) => pr > r^2 + 2 { You can't do this because you don't know p,r are positive or negative}

1) If p = r then r^2 > r^2 + 2[/color]

Using S1, though p = r you still don't know if they are +ve or -ve? Insuff.
Using S2, though r>0 no info about p. Insuff.

Together, if r>0 then p>0 so suff.
Director
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Re: Questions from Gmatprep2 [#permalink] New post 22 May 2008, 17:31
3) From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?

12C1 * 9C2 = 432
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Re: Questions from Gmatprep2 [#permalink] New post 23 May 2008, 10:47
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if the question was asking for at LEAST 1 experienced astronaut, then what would the answer be??

my answer is

combination of all - none

21 C 3 - 9C3 = 1246

Anyone confirm?
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Re: Questions from Gmatprep2 [#permalink] New post 26 May 2008, 21:35
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Nice explanation. But i have a doubt.If c=2 that means it is the diameter. how is possible that two sides are the radii and third one is the diameter. Kindly explain.

I think it can be done in this way: area of a triangle , K=1/2 *a*b*Sin (C)
Since here a,b are constant i.e. 1, The area K is maximum when Sin C is maximum i.e 1
So K=1/2



saravalli wrote:
1) What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
a = b = 1, Also, c < a+b, and c> a-b (from properties of triangle)
Also, r =1. (radius of circle)
So min(c) = 0 and max(c) = 2

Now I googled and found that for a circumscribed triangle,
K = abc / 4r { K is the area of triangle, r is radius of circle }

K will be maximum when c is maximum, because, a,b and r are constant and equal to 1.
K = 1*1*2 / 4*1
K = 1/2.
http://courses.ncssm.edu/goebel/STATECO ... RIANGL.htm
Re: Questions from Gmatprep2   [#permalink] 26 May 2008, 21:35
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