Within the BrainBashers school, the science department has three disciplines.

In total, 280 students study chemistry, 254 students study physics, and 280 students study biology.

In total, 97 students study chemistry and physics, 138 students study physics and biology, and 152 students study chemistry and biology.

73 students study all three disciplines.

Can you determine how many students there are in the science department? The answer is not 814.

Puzzle Copyright © Kevin Stone

workings
hint
answer
print

Share link – www.brainbashers.com/puzzle/zzyu

Hint

How many students study chemistry and physics, but not biology?

Answer

500 students.

Reasoning

The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.

We know that 73 students study all three disciplines, which allows us to work out the numbers.

97 students study chemistry and physics, so 97 - 73 = 24 study just chemistry and physics.

138 students study physics and biology, so 138 - 73 = 65 study just physics and biology.

152 students study chemistry and biology, so 152 - 73 = 79 study just chemistry and biology.

280 students study chemistry, so 280 - 73 - 24 - 79 = 104 study just chemistry.

254 students study physics, so 254 - 73 - 24 - 65 = 92 study just physics.

280 students study biology, 280 - 73 - 65 - 79 = 63 study just biology.

For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.