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Set Theory

by nadib002 » Thu Jun 23, 2011 5:31 am
All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only,how many students are in the orchestra only?

30
51
60
85
119
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by Frankenstein » Thu Jun 23, 2011 5:54 am
Hi,
Let x be the total number of students. Let B and A represent the sets band and orchestra
B only = 0.5x
A only + B only = 0.8x
So, A only = 0.3x
So, A and B = x - (0.8x) = 0.2x

A = Aonly + (A and B) = 0.5x+0.2x = 0.7x
Given that A = 119
So, 0.7x = 119 => x=170
So, A only = 0.3x = (0.3)*170 = 51

Hence, B
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by nadib002 » Thu Jun 23, 2011 7:27 am
Thanks Frankenstein.

Another Set questions:

At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?

20%
25%
50%
75%
80%
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by Frankenstein » Thu Jun 23, 2011 8:20 am
Hi,
Let x and y be the number of red and pink flowers respectively.
One third are short-stemmed(S). So short-stemmed flowers = (1/3)*120 = 40 and long-stemmed are 80.
Red---White---Pink----Total
S--5-----20------15------40
L--(x-5)-0-------(y-15)--80
So, (x-5)+(y-15) = 80 =>x+y =100
Given that The percentage of pink roses that were short-stemmed equal to percentage of red roses that were short-stemmed.
So, 5/x = 15/y =>y = 3x
So, y=75, x=25.
Percentage of long-stemmed roses that were red = 100*(x-5)/80 = (20/80)*100 = 25%

Hence, B

PS: Please post only one question in a thread so that it will be easy for people to check.
Cheers!

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by nadib002 » Fri Jun 24, 2011 5:17 am
Hello Frankenstein:


How did you get 5/x = 15/y. This is where i got stuck. Could you please explain?


Thank you
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by nadib002 » Fri Jun 24, 2011 5:26 am
Frankenstein,

Please ignore my question in the previous post. I got it

Thank you and i will make sure to start a new thread for each new question
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by Frankenstein » Fri Jun 24, 2011 5:28 am
nadib002 wrote:Frankenstein,

Please ignore my question in the previous post. I got it

Thank you and i will make sure to start a new thread for each new question
Glad that you understood that part. I am not 100% convinced about the wording of the question. So, it is natural for anyone to get confused.
Cheers!

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