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In Washington School, 150 students study physics or biology

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In Washington School, 150 students study physics or biology [#permalink] New post 15 Mar 2012, 16:04
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In Washington School, 150 students study physics or biology or both. If 60 of these students do not study biology, how many of these students study both physics and biology?

(1) Of the 150 students, 40 do not study physics.
(2) A total of 110 of the students study physics.

I understand the rest of the question apart from the highlighted text. Can someone please try to explain where it fits in the table please? And also, I will appreciate if you can also please let me know how to get D as an answer.
[Reveal] Spoiler: OA

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Re: Students who study both? [#permalink] New post 15 Mar 2012, 19:48
In Washington School, 150 students study physics or biology or both. If 60 of these students do not study biology, how many of these students study both physics and biology?

(1) Of the 150 students, 40 do not study physics.
(2) A total of 110 of the students study physics.

AD|BCE

A:
Draw a Venn diagram. 60 of these students do not study biology therefore 60 are exclusively physics students. 40 do not study physics therefore 40 are exclusively biology students. This leaves 50 remaining students that study both.

Since A is confirmed, we evaluate B alone...

B: I started off by drawing a Venn diagram for this one too. If 60 of these students do not study biology then they must do physics (same start as A). Now the statement says a total of 110 students study physics so 110-60= 50. These remaining 50 must study both.

A and B are both valid therefore D is the answer. Please let me know if I'm missing something. Hope that helps.
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Re: Students who study both? [#permalink] New post 16 Mar 2012, 02:03
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enigma123 wrote:
In Washington School, 150 students study physics or biology or both. If 60 of these students do not study biology, how many of these students study both physics and biology?

(1) Of the 150 students, 40 do not study physics.
(2) A total of 110 of the students study physics.

I understand the rest of the question apart from the highlighted text. Can someone please try to explain where it fits in the table please? And also, I will appreciate if you can also please let me know how to get D as an answer.


In Washington School, 150 students study physics or biology or both. If 60 of these students do not study biology, how many of these students study both physics and biology?

"150 students study physics or biology or both" means: 150={physics}+{biology}-{both}, we subtract {both} (students who study both physics or biology) since its counted in {physics} as well as in {biology}.

"60 of these students do not study biology" means: 60={physics}-{both} (so 60 study ONLY physics) --> 150=60+{biology} (from above) --> {biology}=90.

Question: {both}=?

(1) Of the 150 students, 40 do not study physics --> 40={biology}-{both} --> 40=90-{both} --> {both}=50. Sufficient.

(2) A total of 110 of the students study physics --> {physics}=110, so from 60={physics}-{both} --> {both}=50. Sufficient.

Answer: D.
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Re: In Washington School, 150 students study physics or biology [#permalink] New post 16 Mar 2012, 02:29
+1 D

I used the ven dig to solve this

Got P=110 in the first statement & this is also given in the 2nd statement. Thus D
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Re: In Washington School, 150 students study physics or biology   [#permalink] 16 Mar 2012, 02:29
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