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

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Math Expert
Joined: 02 Sep 2009
Posts: 55237
At a garage sale, the prices of all the items sold were different. The  [#permalink]

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02 Jul 2017, 02:09
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:22) correct 33% (02:19) wrong based on 55 sessions

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At a garage sale, the prices of all the items sold were different. The items sold were radios and DVD players. If the price of a radio sold at the garage sale was the 15th highest price as well as the 20th lowest price among the prices of the radios sold, and the price of a DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold, how many DVD players were sold at the garage sale?

(A) 30
(B) 31
(C) 32
(D) 64
(E) 65

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

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02 Jul 2017, 02:11
Bunuel wrote:
At a garage sale, the prices of all the items sold were different. The items sold were radios and DVD players. If the price of a radio sold at the garage sale was the 15th highest price as well as the 20th lowest price among the prices of the radios sold, and the price of a DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold, how many DVD players were sold at the garage sale?

(A) 30
(B) 31
(C) 32
(D) 64
(E) 65

This is a modified question of the the following OG question: https://gmatclub.com/forum/at-a-garage- ... 67090.html
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Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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02 Jul 2017, 06:42
Imo C
From the given information we have DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold Total number of items sold =29+37-1 =65
So no DVD players sold =65-34=31
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Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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14 Jul 2017, 04:48
2
Bunuel wrote:
At a garage sale, the prices of all the items sold were different. The items sold were radios and DVD players. If the price of a radio sold at the garage sale was the 15th highest price as well as the 20th lowest price among the prices of the radios sold, and the price of a DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold, how many DVD players were sold at the garage sale?

(A) 30
(B) 31
(C) 32
(D) 64
(E) 65

Responding to a pm:

Prices of all items are different. Think of putting them on a list in decreasing order.

"the price of a DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold"
- So a DVD player is 29th on the list and 37th from bottom. So it has another 36 items under it. This means there are a total of 29 + 36 = 65 items on the list.

Now consider doing the same for only the radios.
"If the price of a radio sold at the garage sale was the 15th highest price as well as the 20th lowest price among the prices of the radios sold"
- So a radio is 15th on the list and has 19 other radios under it. So there are a total of 15+19 = 34 radios.

This means we have 65 - 34 = 31 radios.
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At a garage sale, the prices of all the items sold were different. The  [#permalink]

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14 Jul 2017, 05:05
Bunuel wrote:
At a garage sale, the prices of all the items sold were different. The items sold were radios and DVD players. If the price of a radio sold at the garage sale was the 15th highest price as well as the 20th lowest price among the prices of the radios sold, and the price of a DVD player sold was the 29th highest price as well as the 37th lowest price among all the prices of all the items sold, how many DVD players were sold at the garage sale?

(A) 30
(B) 31
(C) 32
(D) 64
(E) 65

We need to deduct the number of radios from total number of items, which includes DVD, then everything falls into its proper place.

Price of a radio was 15th from the top of the list and 20th from the bottom of the list (among the prices of the radios sold), so the total number of radios = $$15+20-1$$ (deduct 1 to avoid double-counting) = $$34$$.

Price of a DVD was 29th from the top of the list and 37th from the bottom of the list (among the prices of ALL ITEMS sold), so the total number of items = $$29+37-1 = 65$$.

So, the number of DVD players alone = $$65-34 = 31$$. Ans - B.
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At a garage sale, the prices of all the items sold were different. The   [#permalink] 14 Jul 2017, 05:05
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