Which reaction is useful to prepare odd number of hydrocarbons?
The Corey–House reaction constitutes a general and high yielding method for the joining of two alkyl groups or an alkyl group and an aryl group.



Step one involves preparation of the Gilman reagent from an alkyl halide.


$$\ce{R–X + 2Li -&gt; RLi + Li+X–}$$


Second step, a lithium dialkylcuprate (Gilman reagent) is prepared from the alkyllithium by treatment with cuprous iodide (CuI).


$$\ce{2RLi + CuI -&gt; Li+[R–Cu–R]– + LiI}$$


The third step ,involvs reaction between lithium dialkylcuprate (Gilman reagent) and a second alkyl halide ,resulting in the formation of a C–C bond between the two organic fragments:


$$\ce{Li+[R–Cu–R]– + R'–X -&gt; R–R' + "RCu" + LiX}$$

Example 1

In the following example, gem dihalides react with $\ce{Li+[CH_3–Cu–CH_3]– }$ to give the final product. You could read about it in wikipedia

 

Example 2



source

Reference

1.https://en.wikipedia.org/wiki/Corey%E2%80%93House_synthesis

2.https://www.synarchive.com/named-reactions/corey-posner-whitesides-house-reaction