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

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Re: At a garage sale, the prices of all the items sold were different. The [#permalink]
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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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This is an interesting question with a fair bit of logical reasoning built into the question.

An approach that always works in such questions is to use the number line to represent the prices and determine the exact positions of each item. The following diagrams depict how this can be done:

Attachment:

3rd Dec 2019 - Reply 1.jpg [ 47.9 KiB | Viewed 3818 times ]

If a particular radio is the 15th highest, it means that there are 14 radios above it in terms of price; similarly, there are 19 radios that are below it since the same radio is the 20th lowest.
Therefore, total number of radios = 14 + 1 + 19 = 34.

Similarly, if a particular DVD player is the 29th highest article, it means that there are 28 articles above it in terms of price; similarly, there are 36 articles that are below it since the same DVD player is the 37th lowest article.
Therefore, total number of articles = 28 + 1 + 36 = 65.

Of 65 total articles, if 34 are radios, the remaining 31 have to be DVD players.
The correct answer option is B.

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

To understand the approach for solving this problem, consider the situation in which there are only 5 radios, listed in decreasing order of sales price: A B C D E. We see that radio D is the fourth highest in sales price, and it is also the second lowest in sales price. To calculate the total number of radios just from these two pieces of information, we see that we add the two values (4 and 2), but then we must subtract 1, since we double-counted radio D. Thus, we know that there are 4 + 2 - 1 = 5 total radios.

For the given problem, we see that there are 20 + 15 - 1 = 34 radios and 29 + 37 - 1 = 65 total items, so there are 65 - 34 = 31 DVD players.

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