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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: 59588
At a garage sale, the prices of all the items sold were different. The  [#permalink]

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27 Sep 2018, 05:32
1
1
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Difficulty:

55% (hard)

Question Stats:

46% (01:42) correct 54% (02:02) wrong based on 39 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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Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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

Total items sold = 37 + 29 -1 = 65

65 - 34 = 31

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Manager
Joined: 14 Jun 2018
Posts: 211
Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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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
VP
Joined: 09 Mar 2016
Posts: 1229
At a garage sale, the prices of all the items sold were different. The  [#permalink]

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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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Posts: 24
Location: Saudi Arabia
GPA: 3.8
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Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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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
Manager
Joined: 14 Jun 2018
Posts: 211
Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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30 Sep 2018, 11:52
1
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.
VP
Joined: 09 Mar 2016
Posts: 1229
Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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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 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
Intern
Joined: 25 Nov 2019
Posts: 10
Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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

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CrackVerbal Quant Expert
Joined: 12 Apr 2019
Posts: 313
Re: At a garage sale, the prices of all the items sold were different. The  [#permalink]

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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 [ 47.9 KiB | Viewed 71 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] 03 Dec 2019, 00:15
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