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

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Manager
Joined: 06 Feb 2010
Posts: 146
Schools: University of Dhaka - Class of 2010
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At a garage sale, all of the prices of the items sold were  [#permalink]

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23 Oct 2010, 05:53
3
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:02) correct 22% (01:22) wrong based on 249 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/at-a-garage- ... 67090.html

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

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23 Oct 2010, 05:57
1
14+19+1= 34

(20th lowest means 19 items are below it, 15th highest means 14 items are above it)
Intern
Joined: 19 Nov 2011
Posts: 7
Re: At a garage sale, all of the prices of the items sold were  [#permalink]

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Updated on: 28 Jan 2012, 04:26
1
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

Originally posted by RadhaKrishnan on 28 Jan 2012, 04:06.
Last edited by Bunuel on 28 Jan 2012, 04:26, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 54401
Re: At a garage sale, all of the prices of the items sold were  [#permalink]

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28 Jan 2012, 04:25
2
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.

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Posts: 54401
Re: At a garage sale, all of the prices of the items sold were  [#permalink]

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28 Jan 2012, 05:23
3
Why do we add -1 ?

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

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21 Jun 2016, 07:59
start the items with ascending prices

1,2,3,4,5......20th lowest and 15 highest, 14 highest ,13 highest.

this way would be more easy

so, 20 +14 more to go=34

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

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21 Jun 2016, 08:22
4
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

If price of a radio is 15th highest and 20th lowest, than there are 14 items with price lower than Radio's price and 19 items with price higher than Radio's price.

Total items= 14+1+19= 34

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

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30 Oct 2016, 11:11
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

If price of a radio is 15th highest and 20th lowest, than there are 14 items with price lower than Radio's price and 19 items with price higher than Radio's price.

Total items= 14+1+19= 34

Amazing solution, Thanks.
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Manager
Status: Quant Expert Q51
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Re: At a garage sale, all of the prices of the items sold were  [#permalink]

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30 Oct 2016, 12:46
There was 14 items below his price and 19 higher. so 14+19= 33 we have to add him also. so 33+1= 34

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Posts: 54401
Re: At a garage sale, all of the prices of the items sold were  [#permalink]

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02 Jul 2017, 02:08
monirjewel wrote:
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/at-a-garage- ... 67090.html
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Re: At a garage sale, all of the prices of the items sold were   [#permalink] 02 Jul 2017, 02:08
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