A school wants all of the students to take at least one science lectur

Question

A school wants all of the students to take at least one science lecture among Physics, Chemistry, and Biology. 30 students took Physics, 25 students took Chemistry, and 17 students took Biology. 2 students took three lectures. 7 students took Physics and Chemistry, 6 students took Chemistry and Biology, 8 students took Biology and Physics. How many students took only 1 science lecture?

A. 33
B. 36
C. 41
D. 51
E. 57

A. 33
B. 36
C. 41
D. 51
E. 57

Abhishekgmat87 · Answer

Please refer the venn diagram. 7 students took physics and chemistry. No. of students who took physics and chemistry but not bio is 7-2 = 5. Same way, we get 4 students for chemistry and bio only, 6 students for bio and physics only.

Option B

poorvi125 · Answer

Bunuel 
 ThatDudeKnows

Please guide. How do I know here that when the question says 7 students took Physics and Chemistry, the number 7 is not inclusive of the such students who took all the three subjects?
What is the approach to be followed for such questions?

ThatDudeKnows · Answer

poorvi125

The 7 IS inclusive of the 2 who took all three.

People houses, cars, and boats.
Two people own a house a car and a boat.
Seven people own a house and a car. 
How should we draw that? Which of the attached fits?
The one on the left looks good. The one on the right means that NINE people own a house and a car, so that's incorrect. 
Can you use that to draw a diagram to solve the original question?

AaryanK · Answer

GMATNinja 
Can you show this using the matrix approach?

Charli08 · Answer

I also prefer the matrix approach much more over the ven diagrams, but I don't think (at least to my knowledge) that you can use it when you have sets of 3.

Chanovski · Answer

Why is it 19 and not 17 for P?

JeffTargetTestPrep · Answer

#Physics only = #Physics – #Physics and Chemistry – #Biology and Physics + #All 3 = 30 – 7 – 8 + 2 = 17

#Chemistry only = #Chemistry – #Physics and Chemistry – #Chemistry and Biology + #All 3 = 25 – 7 – 6 + 2 = 14

#Biology only = #Biology – #Chemistry and Biology – #Biology and Physics + #All 3 = 17 – 6 – 8 + 2 = 5

Total number of members in exactly one group = #Physics only + #Chemistry only + #Biology only = 17 +14 + 5 = 36

Answer: B

Can,Will · Answer

KarishmaB   Bunuel   gmatophobia

only 1 science lecture = Total - two lectures - three lectures

I tried by this approach but got wrong answer.

total= A+B+C-( SUM OF TWO) + all three + neither 
i got 53 as total .

then ,53- twos -threes

KarishmaB · Answer

I would do it using a Venn diagram only and not formulae, but if you must use formulae, here is how you will do it  Can,Will

Here, None = 0 because everyone must take at least one science lecture.

Total number of students = 30 + 25 + 17 - (7 + 6 + 8) + 2 = 53

53 = Exactly 1 lecture + Exactly 2 lectures + Exactly 3 lectures

53 = Exactly 1 lecture + (7 - 2 + 6 - 2 + 8 - 2) + 2

Exactly 1 lecture = 53 - 17 = 36

Answer (B)

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A school wants all of the students to take at least one science lectur

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A school wants all of the students to take at least one science lectur

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