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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 » Tue Sep 04, 2018 6:07 am

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GMAT Paper Tests

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

OA B.
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by Brent@GMATPrepNow » Tue Sep 04, 2018 6:33 am
AAPL wrote:GMAT Paper Tests

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

OA B.
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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At a garage sale, all of the prices of the items sold were d

by fskilnik@GMATH » Tue Sep 04, 2018 8:11 am
AAPL wrote:GMAT Paper Tests
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
A simple drawing does the trick!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

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by Scott@TargetTestPrep » Tue Oct 02, 2018 6:25 pm
AAPL wrote:GMAT Paper Tests

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 a price higher than the radio, and 19 items have a 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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