Ah, aspirin!
This has the formula C9H8O4.
We draw the Lewis structure (you can see it here):
http://en.wikipedia.org/wiki/Acetylsalicylic_acid
and every single bond is a sigma, a double bond is a sigma and a pi and a triple is a sigma and two pi.
You just want pi bonds and there are no triple bonds, so just count the double bonds.
There are five, so there are FIVE pi bonds present my young chemist!
CH3COOH has 7 sigma bonds, they are all the C-H bonds (3 total), C-C bond (1 total), C-O bond (1 total), O-H bond (1 total) and one from the C=O. It has 1 pi bond which is the C=O bond. So the answer is E. I hope this helps.
5 , 3 for the benzene ring , 1 for the acetyl group, 1 for the acid
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