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

Question

In a freshman high school class there are 125 total students. If 75 of the total students are enrolled in Geometry, how many students are enrolled in Biology?

(1) 50 of the total students are enrolled in Geometry but not Biology.

(2) The number of those students who are enrolled in Geometry and Biology is the same as the number of those students enrolled in neither Geometry nor Biology.

EMPOWERgmatRichC · Accepted Answer

Hi cg0588,

Yes, you CAN use the Tic-Tac-Toe Board to answer this question. Here's how:

Attachment:

GCTTTBoard.png [ 452.06 KiB | Viewed 18898 times ]

From the prompt, you have enough information to fill in the right-most column. We're asked to find the value in the lower-left corner.

Fact 1: 50 students are in Geometry, but NOT Biology.

This Fact gives us the upper-middle box, which we can use to figure out the upper-left box. Unfortunately, it's not enough info to answer the question.
Fact 1 is INSUFFICIENT.

Fact 2: The same number of students are enrolled in BOTH classes as are enrolled in NEITHER of the classes.

Let's call the number of students X...so we have X in two of the boxes.

Working on the second row, we have ___ + X = 50, so the ____ must be (50-X)

Now, using the first column, we have (X) + (50-X). The +X and -X cancel out and we're left with 50.
Fact 2 is SUFFICIENT.

Final Answer:

Show Spoiler

B

GMAT assassins aren't born, they're made,
Rich

Gnpth · Answer

Before we get into the solutions, please read the forum rules before posting a questions. It was posted in PS forum, but this is a DS question. I have moved it to DS forum Now on the solution, Total=125. Geometry or G= 75, and we need to find Biology or Bio. St1: It says only 50 student are enrolled for only G but not Bio. That means there are 25 student in both. But we don't know, how many students enrolled in neither of these subject. So insufficient. St2: Its says Neither(N)= Both(B). So 75+ Bio+N-B=125, we know N=B. So it cancels each other. 75+Bio=125. Bio= 50. Sufficient. Hope it helps

.

thefibonacci · Answer

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.

cg0588 · Answer

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

cg0588 · Answer

EMPOWERgmatRichC  - thanks!

GDT · Answer

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!

minustark · Answer

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.

KarishmaB · 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.

Basshead · Answer

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.

rvgmat12 · Answer

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).

bumpbot · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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