The dibromide shown is treated with sodium in dry ether, and the organic product is examined by ${}^1$H NMR. How many signals does the product show?

The compound shown is 1,3-dibromo-2,2-dimethylpropane. Intramolecular Wurtz coupling joins the two $\mathrm{CH}{}_2\mathrm{Br}$ carbons to give 1,1-dimethylcyclopropane. Its six methyl hydrogens are equivalent and its four ring $\mathrm{CH}{}_2$ hydrogens are equivalent, so there are 2 signals.