At a special sale, all of the prices of the items were different. If

Question

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

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

Archit3110 · Answer

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

Akp880 · Answer

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

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

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

Abhishek009 · Answer

|---------------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

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

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

Kimberly77 · Answer

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 ,  ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?

BrentGMATPrepNow · Answer

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)

Kimberly77 · Answer

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?

BrentGMATPrepNow · Answer

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.

Kimberly77 · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

At a special sale, all of the prices of the items were different. If

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At a special sale, all of the prices of the items were different. If

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards