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

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%

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.

Hello Frankenstein:


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


Thank you

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

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.