At a special sale, all of the prices of the items were different. If : Problem Solving (PS)

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Bunuel

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

15 Sep 2020, 08:00

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At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

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Archit3110

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

15 Sep 2020, 08:05

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Kudos

Bunuel wrote:

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

considering that radio is placed in sequence of increasing price we get 14 items below radio and
when radio is placed in descending order its at 20th place
total items 14+20 ; 34
OPTION B

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

15 Sep 2020, 08:11

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

Explanation:

As given radio price was 20th lowest and 15th highest

Implies, if we arrange prices in ascending order>>>

There will be 19 items before and 14 items ahead of given radio piece

So total item sold

=19+1+14

=34

Hence B is the correct answer.

Regards,
Atul Pandey

Posted from my mobile device

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BrentGMATPrepNow

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Location: Canada

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

25 Nov 2020, 11:48

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Bunuel wrote:

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

Let x = the price of the radio

The price of a radio sold at the sale was the 15th highest price
So, if all of the prices were written in ASCENDING order, then there would be 14 items that are more expensive than x (the price of the radio)
In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

The price of a radio sold at the sale was the 20th lowest price
So, if all of the prices were written in ASCENDING order, then there would be 19 items that are less expensive than x (the price of the radio)
In other words, our list would look like this: ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?,x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

How many items were sold at the sale?
TOTAL number of items = 19 + 1 + 14 = 34

Answer: B

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

30 Nov 2020, 10:13

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Bunuel wrote:

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

Solution:

Since the radio had the 15th highest price, 14 items had a price higher than the radio. Likewise, since the radio had the 20th lowest price, 19 items had a price lower than the radio. Therefore, there were 14 + 1 + 19 = 34 items sold at the sale.

Answer: B
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Kinshook

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

30 Nov 2020, 10:31

Given: At a special sale, all of the prices of the items were different.
Asked: If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

If we arrange prices of all the items in descending order, we get
14 items - Radio - 19 items
Total items sold = 14 + 1 + 19 = 34

IMO B

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Abhishek009

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

30 Nov 2020, 10:51

Bunuel wrote:

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

|---------------19 items-------------Item---------14 items----------|

19 + 14 = 33 items...

Now, you are actually counting the middlemost item twice , once when counting highest & once while counting lowest, hence we must add 1 item!!!

Thus, correct Answer must be (B) 34
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Kimberly77

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Joined: 16 Nov 2021

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Location: United Kingdom

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

29 Jan 2023, 02:55

BrentGMATPrepNow wrote:

Bunuel wrote:

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

Let x = the price of the radio

The price of a radio sold at the sale was the 15th highest price
So, if all of the prices were written in ASCENDING order, then there would be 14 items that are more expensive than x (the price of the radio)
In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

The price of a radio sold at the sale was the 20th lowest price
So, if all of the prices were written in ASCENDING order, then there would be 19 items that are less expensive than x (the price of the radio)
In other words, our list would look like this: ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?,x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

How many items were sold at the sale?
TOTAL number of items = 19 + 1 + 14 = 34

Answer: B

Hi BrentGMATPrepNow, silly question that isn't x show as the 1st of the position and ? at the end is the 15th highest in ascending order? not sure what did I miss? Thanks Brent

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BrentGMATPrepNow

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Joined: 12 Sep 2015

Posts: 6822

Location: Canada

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

29 Jan 2023, 11:10

Expert Reply

Top Contributor

Kimberly77 wrote:

BrentGMATPrepNow wrote:

Bunuel wrote:

At a special sale, all of the prices of the items were different. If the price of a radio sold at the sale was both the 15th highest and the 20th lowest price among the prices of the items sold, how many items were sold at the sale?

A. 33
B. 34
C. 35
D. 36
E. 37

Let x = the price of the radio

The price of a radio sold at the sale was the 15th highest price
So, if all of the prices were written in ASCENDING order, then there would be 14 items that are more expensive than x (the price of the radio)
In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

The price of a radio sold at the sale was the 20th lowest price
So, if all of the prices were written in ASCENDING order, then there would be 19 items that are less expensive than x (the price of the radio)
In other words, our list would look like this: ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?,x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

How many items were sold at the sale?
TOTAL number of items = 19 + 1 + 14 = 34

Answer: B

Hi BrentGMATPrepNow, silly question that isn't x show as the 1st of the position and ? at the end is the 15th highest in ascending order? not sure what did I miss? Thanks Brent

Sorry, can you please rephrase your question?
I'm not sure what you are asking.

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Kimberly77

Senior Manager

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Posts: 476

Location: United Kingdom

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

01 Feb 2023, 12:43

Sure BrentGMATPrepNow, I mean according to below:

Isn't x show as the 1st of the position and ? at the end is the 15th highest in ascending order?

In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

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BrentGMATPrepNow

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Posts: 6822

Location: Canada

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

02 Feb 2023, 17:12

Expert Reply

Top Contributor

Kimberly77 wrote:

Sure BrentGMATPrepNow, I mean according to below:

Isn't x show as the 1st of the position and ? at the end is the 15th highest in ascending order?

In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

That part is just the beginning of my solution, where I show that x is the 15th highest in ascending order?
In other words, if x is the 15th highest price, then there are 14 values that are greater than x (thus the 14 ?'s)

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Kimberly77

Senior Manager

Joined: 16 Nov 2021

Posts: 476

Location: United Kingdom

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

04 Feb 2023, 12:17

BrentGMATPrepNow wrote:

Kimberly77 wrote:

Sure BrentGMATPrepNow, I mean according to below:

Isn't x show as the 1st of the position and ? at the end is the 15th highest in ascending order?

In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

That part is just the beginning of my solution, where I show that x is the 15th highest in ascending order?
In other words, if x is the 15th highest price, then there are 14 values that are greater than x (thus the 14 ?'s)

Thanks BrentGMATPrepNow. If x is the 15th highest price, not sure why it doesn't mean there are 14 values lowver than 15th but greater here?

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BrentGMATPrepNow

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Joined: 12 Sep 2015

Posts: 6822

Location: Canada

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

05 Feb 2023, 07:55

Expert Reply

Top Contributor

Kimberly77 wrote:

BrentGMATPrepNow wrote:

Kimberly77 wrote:

Sure BrentGMATPrepNow, I mean according to below:

Isn't x show as the 1st of the position and ? at the end is the 15th highest in ascending order?

In other words, our list would look like this: ........x, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

That part is just the beginning of my solution, where I show that x is the 15th highest in ascending order?
In other words, if x is the 15th highest price, then there are 14 values that are greater than x (thus the 14 ?'s)

Thanks BrentGMATPrepNow. If x is the 15th highest price, not sure why it doesn't mean there are 14 values lowver than 15th but greater here?

Sorry, but that's just what those words mean.
For example, if someone is the 2nd tallest person in the world, then that means there's only 1 person taller.
Similarly, if someone is the 15th tallest person in the world, then that means there are 14 people who are taller.

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Kimberly77

Senior Manager

Joined: 16 Nov 2021

Posts: 476

Location: United Kingdom

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

07 Feb 2023, 14:22

Ah your explanation is great and crystal clear as always...make sense now. Thanks BrentGMATPrepNow.

gmatclubot

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

07 Feb 2023, 14:22

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