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### Dr Penny Pincher says

I would say c, 90

You can assume:

Sci + arts + comm = 270

Then substitute to put everything in terms of science students:

Remember to scale art and comm students to the full population, not 3/4 and 3/5.

Nice puzzle!

### TR Smith says

If everyone is in exactly one of the three streams, then you solve the system

S + A + C = 270

(2/3)S = (3/4)A

(2/3)S = (3/5)C

The last two equations are equivalent to (8/9)S = A and (10/9)S = C. If you substitute those into the first equation, you get

S + (8/9)S + (10/9)S = 270

3S = 270

S = 90.

So the answer is choice c.