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# At a garage sale, all of the prices of the items sold were d

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Math Expert
Joined: 02 Sep 2009
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At a garage sale, all of the prices of the items sold were d  [#permalink]

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05 Feb 2014, 02:31
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Question Stats:

75% (01:09) correct 25% (01:27) wrong based on 947 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

Problem Solving
Question: 80
Category: Arithmetic Operations with integers
Page: 72
Difficulty: 600

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

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05 Feb 2014, 02:31
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SOLUTION

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

As the price of an item was BOTH 15th highest price and the 20th lowest price then # of items is: 15 + 20 - 1 = 34.

Why do we have -1 there? In 15 + 20 the item is counted TWICE: in 15 (as it's 15th highest priced item) as well as in 20 (as it's 20th lowest priced item), hence we should subtract 1 to get rid of double counting.

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

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05 Feb 2014, 08:27
1
Ans B

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

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07 Feb 2014, 13:36
2
I got (B) too. However, is it correct to use this approach?

20+15-1 (to avoid double-counting) = 34.
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Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

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07 Feb 2014, 21:42
I am not clear how to solve this problem.... Can any one detail out... thanks
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Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

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08 Feb 2014, 04:14
SOLUTION

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

As the price of an item was BOTH 15th highest price and the 20th lowest price then # of items is: 15 + 20 - 1 = 34.

Why do we have -1 there? In 15 + 20 the item is counted TWICE: in 15 (as it's 15th highest priced item) as well as in 20 (as it's 20th lowest priced item), hence we should subtract 1 to get rid of double counting.

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

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18 May 2015, 03:33
1
There are 14 objects that have a higher price as the radio, as well as 19 objects that have a lower price than the radio.

14 + 19 + 1 (the radio itself) = 34 different objects
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Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

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03 Jul 2017, 12:07
At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

Given: Price of Radio is 15th Heighest and 20th Lowest

Which means form top if you count price will be 15th and if you count from bottom the count will be 20th.

So, from top it is 15th and there are 19 more items below the list (As this is 20th from bottom)

Hence, 15 + 19 = 34

So, in all there were 34 items sold at the garage.

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

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29 Mar 2018, 17:38
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Bunuel wrote:

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

Since the radio is the 15th highest and 20th lowest we see that 14 items have price higher than the radio and 19 items have price lower than the radio, so the total number of items at the sale is 14 + 19 + 1 = 34. (Note that the +1 item is the radio itself.)

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

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31 Mar 2018, 06:50
2
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

The price of the radio was the 15th highest price
So, there were 14 items that were more expensive than the radio.
In other words, if we listed all of the prices in ascending order, we'd get something like:
........... radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X

The price of the radio was the 20th lowest price
So, there were 19 items than were less expensive than the radio.
In other words, if we listed all of the prices in ascending order, we'd get something like:
X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, radio,......

So, when we combine both pieces of information, we have 19 items that were less expensive than the radio, and we have 14 items that were more expensive than the radio:
X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X

So, the total number of items sold = 19 + 14 + 1 (the radio itself)
= 34
= B

Cheers,
Brent
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At a garage sale, all of the prices of the items sold were d  [#permalink]

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04 Sep 2018, 09:31
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

A simple drawing does the trick!

? = 20+14 = 34.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

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29 Sep 2018, 10:56
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

Problem Solving
Question: 80
Category: Arithmetic Operations with integers
Page: 72
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

If it is the 15th it means there are 14 higher in price and if it is 20th it means there are 19 that are lower in price

Adding these two we get 14+19+1 = 34, the one here is added to include the radio itself.

Or 20+15 - 1 = 34

Re: At a garage sale, all of the prices of the items sold were d   [#permalink] 29 Sep 2018, 10:56
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