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

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

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New post 27 Sep 2018, 05:32
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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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New post 30 Sep 2018, 11:52
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vipulshahi wrote:
Dear dave13,

Can you please explain the logic behind this question.

Why are you deducting lowest DVD from lowest Radio and Highest DVD from highest Radio.

Thank you


take a small example

A B C D E F

Here D is 4th highest and 3rd lowest. 4+3 - 1 = 6 items in total. We subtract 1 because D is being counted twice.
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Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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New post 27 Sep 2018, 07:05
Total number of radios sold = 15 + 20 - 1 = 34

Total items sold = 37 + 29 -1 = 65

65 - 34 = 31

Answer choice B

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

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New post 27 Sep 2018, 11:00
Radios = 20+15 -1 = 34 (That particular radio is being counter twice so -1)
Total items = 29 + 37 - 1 = 65

Total dvd's = 65-34 = 31
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At a garage sale, the prices of all the items sold were different. The  [#permalink]

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New post 27 Sep 2018, 12:04
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


At first glance I got confused but after some time i figured out how to solve it :)

so the logic here is to subtract lowest DVD from lowest Radio and Highest DVD from highest Radio

\(37 - 20 = 17\)
\(29 - 15 = 14\)

\(17+14 = 31\)
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Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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New post 30 Sep 2018, 11:23
Dear dave13,

Can you please explain the logic behind this question.

Why are you deducting lowest DVD from lowest Radio and Highest DVD from highest Radio.

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

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New post 30 Sep 2018, 12:22
vipulshahi wrote:
Dear dave13,

Can you please explain the logic behind this question.

Why are you deducting lowest DVD from lowest Radio and Highest DVD from highest Radio.

Thank you



vipulshahi thank you for your question :) sure I will gladly explain you my reasoning, though my logic is not standard it doesn't follow sometimes standard approaches :lol: and I don`t want to confuse you even more:)

HIGHEST PRICES 'DVDs \(x_1\)and RADIO \(x_2\) ---> \(x_1 - x_2\)


LOWEST PRICES 'DVDs \(y_1\) and RADIO \(y_2\) ----> \(y_1 - y_2\)

:) thats it

i think approaches above are more logical than mine :)
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Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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New post 02 Dec 2019, 19:37
Turns out it doesn’t matter if you -1 as long as you are consistent

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

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New post 03 Dec 2019, 00:15
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
3rd Dec 2019 - Reply 1.jpg [ 47.9 KiB | Viewed 223 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]

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New post 12 Jan 2020, 06:29
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.

Answer: B
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Re: At a garage sale, the prices of all the items sold were different. The   [#permalink] 12 Jan 2020, 06:29
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