I answered '1.'
It was a Malcolm Gladwell "Blink" answer. I didn't ponder my decision at all. Doesn't make my answer correct, but it does prevent me from getting sucked into a self debate. Here's my logic:
We make the equation a bit more algebraic without changing the operators and parens:
c/2(a+b) where a=1, b=2, and c=6
If you assume c/2 comes after evaluating (a+b), you are essentially putting (a+b) in the numerator of your division:
c/2 * (a+b)/1 > c(a+b)/2
So if the equation was written as c(a+b)/2 ((a+b) is in the numerator), your final answer is 9. But the equation was definitely not written in this way. So 9 is wrong.
As the original equation was written, (a+b) is clearly in the denominator because I proved above it can't be in the numerator without a drastic rewrite of the equation. In other words, c/2(a+b) can only imply that (a+b) is in the denominator without rewriting the equation. Therefore, as the original equation was written, the answer is the following:
eval parens first: (a+b) = 3
3 is part of the denominator, so 6/2(3) = 6/6 = 1
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The good thing about science is that it's true whether or not you believe in it. Neil deGrasse Tyson
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