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

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AAPL: Moderator; Posts: 2644; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Wed Dec 19, 2018 3:16 am

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GMAT Paper Tests

At 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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Dec 19, 2018 3:36 am

AAPL wrote:GMAT Paper Tests

At 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 = 15th highest price, 14 prices are HIGHER:
RADIO-----14 higher prices----->

Since the radio = the 20th lowest price, 19 prices are LOWER:
<-----19 lower prices-----RADIO-----14 higher prices---->

Total number of items = 19 + RADIO + 14 = 34.

The correct answer is B.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 19, 2018 6:15 am

AAPL wrote:GMAT Paper Tests

At 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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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Dec 19, 2018 7:46 am

AAPL wrote:GMAT Paper Tests

At 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!

\[? = 20+14 = 34\]

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Mar 03, 2019 6:24 pm

AAPL wrote:GMAT Paper Tests

At 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

Since the radio's price 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. Thus, 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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