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

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At garage sale, all of the prices of the items sold were different. If [#permalink]

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23 Oct 2010, 05:53
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Difficulty:

15% (low)

Question Stats:

71% (01:46) correct 29% (01:09) wrong based on 160 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
[Reveal] Spoiler: OA

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

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

(20th lowest means 19 items are below it, 15th highest means 14 items are above it)
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At a garage sale, all of the prices of the items sold were [#permalink]

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28 Jan 2012, 04:06
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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

Last edited by Bunuel on 28 Jan 2012, 04:26, edited 1 time in total.
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28 Jan 2012, 04:25
1
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Expert's post
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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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
KUDOS
Expert's post
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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05 Oct 2013, 07:40
Hello from the GMAT Club BumpBot!

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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, 01:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

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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
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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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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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Re: At a garage sale, all of the prices of the items sold were   [#permalink] 30 Oct 2016, 12:46
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