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

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In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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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.

Originally posted by PathFinder007 on 19 Sep 2014, 22:33.
Last edited by Bunuel on 20 Sep 2014, 01:40, edited 2 times in total.
Moved the topic to correct forum
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Re: In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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New post 19 Sep 2014, 22:55
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PathFinder007 wrote:
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?

A.50 of the total students are enrolled in Geometry but not Biology.

B.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.


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 :).
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Re: In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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New post 26 Sep 2014, 10:08
PathFinder007 wrote:
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.


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.
Attachments

venn.png
venn.png [ 13.32 KiB | Viewed 6455 times ]


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Re: In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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New post 28 Jan 2015, 16:10
Is there a way to solve this using the matrix method?
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Re: In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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New post 28 Jan 2015, 18:20
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Hi cg0588,

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

Attachment:
GCTTTBoard.png
GCTTTBoard.png [ 452.06 KiB | Viewed 6137 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.

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Re: In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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New post 29 Jan 2015, 17:30
EMPOWERgmatRichC - thanks!
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Re: In a freshman high school class there are 125 total students. If 75 of  [#permalink]

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Re: In a freshman high school class there are 125 total students. If 75 of &nbs [#permalink] 22 Sep 2018, 05:32
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