Problem Solving

BTGmoderatorLU wrote: ↑

Thu Jun 03, 2021 9:13 am

Source: GMAT Prep

At a special sale, all the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

The OA is B

Let x = the price of the radio

The price of a radio sold at the sale was the 15th highest price
So, if all of the prices were written in ASCENDING order, then there would be 14 items that are more expensive than x (the price of the radio)
In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

The price of a radio sold at the sale was the 20th lowest price
So, if all of the prices were written in ASCENDING order, then there would be 19 items that are less expensive than x (the price of the radio)
In other words, our list would look like this: ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?,x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

How many items were sold at the sale?
TOTAL number of items = 19 + 1 + 14 = 34

Answer: B