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Q10: If each of the students in a certain mathematics class

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Q10: If each of the students in a certain mathematics class [#permalink] New post 09 Jul 2007, 19:25
Q10:
If each of the students in a certain mathematics class is either a junior or a senior, how many students are in the class?
(1) If one student is to be chosen at random from the class to attend a conference, the probability that the student chosen will be a senior is 4/7.
(2) There are 5 more seniors in the class than juniors.
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 [#permalink] New post 09 Jul 2007, 20:50
C

we can make an equation using (1) and (2):

4/7 = x+5/2x+5

Solve
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 [#permalink] New post 09 Jul 2007, 20:56
St1:
P(senior) = 4/7. We don't now how many students as this is just a ratio.

St2:
s = j+5 -> no other useful information.

Using St1 and St2:
P(senior) = s/j+s = s/s-5+s = s/23-5 = 4/7; s = 20. We can then solve for number j and hence # of students in the class. Ans C
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 [#permalink] New post 10 Jul 2007, 00:50
ywilfred wrote:
St1:
P(senior) = 4/7. We don't now how many students as this is just a ratio.

St2:
s = j+5 -> no other useful information.

Using St1 and St2:
P(senior) = s/j+s = s/s-5+s = s/23-5 = 4/7; s = 20. We can then solve for number j and hence # of students in the class. Ans C


Agreed.....should be 'C'
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 [#permalink] New post 15 Jul 2007, 14:01
(n+5)/(n+n+5) = 4/7
7n + 35 = 8n + 20
n=15; n+5=20

C.
  [#permalink] 15 Jul 2007, 14:01
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