How many stereoisomers are possible for 1,2-dimethyl-4-(propan-2-ylidene)cyclopentane? How many stereoisomers (not counting different conformers) does 1,2-dimethyl-4-(propan-2-ylidene)cyclopentane have?
  
  


I think the answer should be 3. There are two geometrical isomers (cis and trans) considering the two methyl groups on the ring, and the trans isomer will also show optical isomerism as it doesn't have a plane of symmetry. But in my book, the answer is given as 2. Is this a misprint?
In this structure the left hand methyl groups can be on the same side of the ring. This is one stereoisomer. This molecule is not chiral and there is only one isomer with the methyl groups on the same side of the ring.

Initially I assumed that there was only one other isomer: the two methyl groups on the opposite side of the ring. But building models sometimes wrecks intuition. The picture below shows the two possible version with trans (relative to the plane of the ring) methyl groups:



So my initial view was wrong: the molecule is chiral and that gives three total stereoisomers.