Identify the structure

The compound is 1,2-dimethylcyclopropane.

A cyclopropane ring has three carbon atoms. Methyl groups are attached at carbon-1 and carbon-2.

Check for stereogenic centers

At carbon-1 and carbon-2, each carbon is attached to:

• one methyl group,
• one hydrogen,
• one ring carbon on one side,
• one ring carbon on the other side.

Because the two paths around the ring are different due to substitution, both C-1 and C-2 behave as stereogenic centers.

So, naively, with 2 stereocenters, maximum stereoisomers could be: $2^2 = 4$

But we must check for symmetry and meso forms.

Possible configurations

There are two geometrical possibilities:

(i) cis-1,2-dimethylcyclopropane

Both methyl groups are on the same side of the ring plane.

• This form has a plane of symmetry.
• Hence it is achiral.
• So cis gives only one stereoisomer.

(ii) trans-1,2-dimethylcyclopropane

The two methyl groups are on opposite sides of the ring plane.

• This form is chiral.
• It exists as a pair of enantiomers.
• So trans gives two stereoisomers.

Total number of stereoisomers

Therefore, $\text{Total stereoisomers} = 1\,(\text{cis}) + 2\,(\text{trans enantiomers}) = 3$

Evaluate options

• A: One $\to$ incorrect
• B: Four $\to$ incorrect
• C: Two $\to$ incorrect
• D: Three $\to$ correct

Comparison with stored answer

Stored correct answer is D.

Our derived answer is also D (Three).