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.

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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+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

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


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Let \(a\) be the number of ONLY physics, \(b\) the number of ONLY biology and \(c\) the number of both PB.

\(a+b+c=150\) and \(a=60\) so \(b+c=90\), c=?

(1) Of the 150 students, 40 do not study physics. (or study ONLY biology)
\(b=40\) => \(c=50\)
Sufficient

(2) A total of 110 of the students study physics.
\(a+c=100\), \(c=50\)
Sufficient

When they say X, Y or both, do they always mean that Neither is zero? Cause I remember seeing a question where this was stated and then had a surprise when in one of the statements it mentioned that neither had a value. Just wondering what is usually the case with this type of wording.

Thanks for the feedback
Cheers
J

150 students study physics or biology or both means that no one from these 150 studies neither physics or biology. How else?

Can you please post the link to the question you are talking about? Thank you.
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Used a table method to solve.

Kudo if it helps

highlighted text clearly tells us that Neither Physics Nor Biology sector is 0

*****P***NP******
**B**X***Y*****90
**NB*Z***0*****60
*****110*40****150
we can fill rest of elements X,Y and Z .
both option are sufficient.

The highlighted segment in the question makes it easier to find out that there is no 'Neither' case here. Wish GMAT was this encouraging!

There are three sections. Section 1 Physics only. Section 2 Both. Section 3. Biology only.

D0 not study physics = study only biology. Sufficient to complete the equations.

No of physics = Physics only + Both, which gives the other component.

Each statement alone is sufficient
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