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Overlapping Sets

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Overlapping Sets

by piyush2694 » Fri Dec 21, 2018 12:16 am

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C

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E

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Each o f the 105 students in a certain club is either a freshman, a sophomore, or a junior. How many of the students in the club are sophomores?

(1) The ratio of the number of freshmen to the number of sophomores is 1 to 2.
(2) The ratio of the number of freshmen to the number of juniors is 1 to 4.
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Source: — Data Sufficiency |
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by deloitte247 » Sun Dec 23, 2018 12:44 pm

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Your Answer

A

B

C

D

E

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How many of the students in the class are sophomores

Statement 1
Ratio of freshmen to the number of sophomores. Statement 1 is INSUFFICIENT.

Statement 2
Ratio of freshmen to juniors is 1 to 4. There is no information about the sophomore hence statement 2 is INSUFFICIENT.

Both statements combined together
Ratio of freshmen to sophomore to juniors = 1:2:4 = 4+ 2 + 1 = 7

$$\frac{2}{7}\cdot105=\ 30\ sop\hom ore\ students$$
Both statement together are SUFFICIENT.
$$answer\ is\ Option\ C$$
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