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Data Sufficiency

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by danjuma » Sat Oct 02, 2010 9:03 pm
Each of the 105 students in a certain club is either a freshman, sophomore or junior. How many of the students in the club are sophomores?

a. The ratio of the number of freshmen to the number of sophomores is 1 to 2

b.The ratio of the number of freshmen to the number of junior is 1 to 4
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by Rahul@gurome » Sat Oct 02, 2010 10:33 pm
Solution:
Consider first (1) alone.
Ratio of the number of freshmen to the number of sophomores is 1 : 2.
We need more information regarding number of juniors to answer the question.
So (1) alone is not sufficient.

Next consider (2) alone.
Ratio of the number of freshmen to the number of juniors is 1 : 4.
This is not sufficient because we need some information about sophomores as well.
So (2) alone is not sufficient.
Next combine both the statements together and check.
On combining, we have that ratio of the number of freshmen to the number of sophomores to the number of juniors
is 1 : 2 :4.
Or number of sophomores is 2/(1+2+4) = (2/7)*105 = 30.

The correct answer is (C).
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