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At a garage sale, all of the prices of the items sold were

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At a garage sale, all of the prices of the items sold were

by AAPL » Wed Mar 28, 2018 4:34 am
At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

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

The OA is B.

I get the solution as follow,

Price of radio is 15th highest and 20th lowest

Which means from top if you count price will be 15th and if you count from bottom the count will be 20th.

So, from top it is 15th and there are 19 more items below the list (As this is 20th from bottom).

Hence, 15 + 19 = 34.

So in all, there were 34 items sold at the garage.

Is there another strategic approach to solve this PS question? Can any experts help, please? Thanks!
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by Scott@TargetTestPrep » Thu Mar 29, 2018 4:37 pm
AAPL wrote:At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

A. 33
B. 34
C. 35
D. 36
E. 37
Since the radio is the 15th highest and 20th lowest we see that 14 items have price higher than the radio and 19 items have price lower than the radio, so the total number of items at the sale is 14 + 19 + 1 = 34. (Note that the +1 item is the radio itself.)

Answer: B

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by Brent@GMATPrepNow » Sat Mar 31, 2018 5:47 am
AAPL wrote:At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

A. 33
B. 34
C. 35
D. 36
E. 37
The price of the radio was the 15th highest price
So, there were 14 items that were more expensive than the radio.
In other words, if we listed all of the prices in ascending order, we'd get something like:
........... radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X

The price of the radio was the 20th lowest price
So, there were 19 items than were less expensive than the radio.
In other words, if we listed all of the prices in ascending order, we'd get something like:
X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, radio,......

So, when we combine both pieces of information, we have 19 items that were less expensive than the radio, and we have 14 items that were more expensive than the radio:
X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X

So, the total number of items sold = 19 + 14 + 1 (the radio itself)
= 34
= B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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