We know that at a garage sale the price of a radio was both the $\(15^{\text {th \)$ highest price and the $\(20^{\text {th \)$ lowest price amongst the prices of all the items that were sold; we need to find the number of items which were sold at the garage sale.

The radio's price being the $\(15^{\text {th \)$ highest implies that there were 14 items which were priced more than it whereas its (Radio) price being the $\(20^{\text {th \)$ lowest means that there were 19 items which were priced less than it.

So, the total number of items in at the Garage sale $\(=\)$ Number of items price higher than the radio + Number of items priced less than the radio $\(+1=14+19+1=34\)$ ( 1 is added for the radio itself)

Hence the answer is (B).