The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 54 said they had taken physics, 92 said they had taken chemistry and 16 said they had taken both. Eight said they had taken neither. How many recent high school grads were surveyed?

Question

anonymous · Answer

Try a Venn diagram.

anonymous · Answer

Not helping

anonymous · Answer

Actually, from the way it's written it sounds like when it says, "54 had taken physics" it means had taken physics but not chemistry, but that is a simplifying assumption. If true, then you can just add up all the numbers because there is no overlap.

To be safe, though, in case that assumption is false consider the possibility that the 54 who took physics includes the 16 who took both.

anonymous · Answer

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anonymous · Answer

How many recent high school grads were surveyed?

anonymous · Answer

If the 54 who took physics does include the 16 who took both, then 54-16 would be those who took physics but not chemistry. Likewise, you can do a similar operation to subtract the overlap from the chemistry total.

anonymous · Answer

It still really sounds like there is no overlap. From the way it's written, I would just add up all those numbers for the total.

anonymous · Answer

I got 170?

anonymous · Answer

That's what I think it would be too, but you have to make an assumption about the meaning based on the wording of the problem. If indeed the 54 physics and 92 chemistry included the overlap of 16 both, then the total would be (54-16) + (92-16) + 16 + 8 = 138.

anonymous · Answer

Did you check the other problem I posted?

anonymous · Answer

Not yet, I'll go take a look now.

anonymous · Answer

Thank You