Each value in a sample has been transformed by multiplying by 3 and then adding 10. If the original sample had a variance of 4, what is the variance of the transformed sample?

Adding values to each data point does not change the spread. However, multiplying each number by 3 does change the standard deviation by a factor of 3. The variance is the square of the standard deviation, so the overall effect on the variance should be a factor of 9.

You can try this with a set of simple numbers to verify.