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

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Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129078 [0], given: 12194

At a garage sale, all of the prices of the items sold were d [#permalink]

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05 Feb 2014, 02:31
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Difficulty:

15% (low)

Question Stats:

71% (00:53) correct 29% (01:17) wrong based on 508 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 80
Category: Arithmetic Operations with integers
Page: 72
Difficulty: 600

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Kudos [?]: 129078 [0], given: 12194

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129078 [0], given: 12194

Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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05 Feb 2014, 02:31
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SOLUTION

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

As the price of an item was BOTH 15th highest price and the 20th lowest price then # of items is: 15 + 20 - 1 = 34.

Why do we have -1 there? In 15 + 20 the item is counted TWICE: in 15 (as it's 15th highest priced item) as well as in 20 (as it's 20th lowest priced item), hence we should subtract 1 to get rid of double counting.

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Kudos [?]: 129078 [0], given: 12194

Senior Manager
Joined: 20 Dec 2013
Posts: 267

Kudos [?]: 106 [0], given: 29

Location: India
Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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05 Feb 2014, 08:27
Ans B

Kudos [?]: 106 [0], given: 29

Manager
Joined: 11 Jan 2014
Posts: 94

Kudos [?]: 73 [2], given: 11

Concentration: Finance, Statistics
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GPA: 3.77
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Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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07 Feb 2014, 13:36
2
KUDOS
I got (B) too. However, is it correct to use this approach?

20+15-1 (to avoid double-counting) = 34.

Kudos [?]: 73 [2], given: 11

Manager
Joined: 14 Jan 2013
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Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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07 Feb 2014, 21:42
I am not clear how to solve this problem.... Can any one detail out... thanks
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Kudos [?]: 378 [0], given: 30

Math Expert
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Posts: 41892

Kudos [?]: 129078 [0], given: 12194

Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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08 Feb 2014, 04:14
SOLUTION

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

As the price of an item was BOTH 15th highest price and the 20th lowest price then # of items is: 15 + 20 - 1 = 34.

Why do we have -1 there? In 15 + 20 the item is counted TWICE: in 15 (as it's 15th highest priced item) as well as in 20 (as it's 20th lowest priced item), hence we should subtract 1 to get rid of double counting.

_________________

Kudos [?]: 129078 [0], given: 12194

Manager
Joined: 07 Apr 2015
Posts: 180

Kudos [?]: 68 [1], given: 185

Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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18 May 2015, 03:33
1
KUDOS
There are 14 objects that have a higher price as the radio, as well as 19 objects that have a lower price than the radio.

14 + 19 + 1 (the radio itself) = 34 different objects

Kudos [?]: 68 [1], given: 185

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Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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31 May 2017, 03:41
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Re: At a garage sale, all of the prices of the items sold were d [#permalink]

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03 Jul 2017, 12:07
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?

Given: Price of Radio is 15th Heighest and 20th Lowest

Which means form 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.

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Re: At a garage sale, all of the prices of the items sold were d   [#permalink] 03 Jul 2017, 12:07
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