In a freshman high school class there are 125 total students. If 75 of

B.

1) This FS does not tell if all the students have enrolled for these subjects or are there some which have enrolled for neither. Hence insufficient.

2) See figure.

Is there a way to solve this using the matrix method?

EMPOWERgmatRichC - thanks!

VeritasKarishma

Can you pls explain how we can differentiate from the ques's language whether it is a case where we have a possibility of some students studying neither or if it case where none is 0

Thanks in advance!

1) Only can infer no of students who have taken Only Geometry (25). NOT SUFFICIENT

2) 125 = 75 + BIOLOGY - BOTH G AND B - NEITHER G AND B. As per statement, last 2 elements are out as they are equal. So, students enrolled in Biology = 125 - 75 = 50. Sufficient.

B is the answer.

If 'neither' is 0 in a question, they will give you that 'every student is enrolled in at least one of them' or 'each student must select at least one' or 'those are the only two courses offered' or something of the sort.
Saying 20 students in this class study French and 40 study German doesn't mean I can't have 100 students in the class. There are numerous other subjects.

See double matrix method attached.

In overlapping set questions, any time you see "is the same as the number of those" as in B you should be suspicious. At first glance Statement 2 appears insufficient, but we can actually determine the number of students enrolled in Biology using this piece of information.

Answer is B.

Official Explanation: The goal in this question is to determine the total number of people enrolled in Biology.

Since there is no way to determine the breakdown between Biology only and neither, there is no way to determine how many total students are studying biology. Statement (1) is not sufficient.

For the second statement, it is VERY easy to overlook that it is sufficient by itself. Most students will pick C as the information in statement (2) when added to statement (1) makes it clearly sufficient. As you learned in the Data Sufficiency lesson, however, before you pick C, you should examine each one alone very carefully.

For the second statement simply consider the formula: Total = Set 1 + Set 2 – Both + Neither and plug in the information from the question stem and from the statement: 125 = 75 + Biology – x + x. Since both and neither are the same, they will cancel out and the number of students taking Biology must be 50. Answer is (B).

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