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

Question

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

Bunuel · Accepted Answer

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

(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.

Answer: B.

AKG1593 · Answer

Ans B

Total=14 (items with higher price than the radio)+19(items with lower price than radio)+1(radio itself)=34

Abdul29 · Answer

I got (B) too. However, is it correct to use this approach?

20+15-1 (to avoid double-counting) = 34.

HarveyS · Answer

I am not clear how to solve this problem.... Can any one detail out... thanks

noTh1ng · Answer

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

ydmuley · Answer

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

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.

Hence, Answer is B

ScottTargetTestPrep · Answer

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.)

Answer: B

BrentGMATPrepNow · Answer

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

fskilnik · Answer

A simple drawing does the trick!

? = 20+14 = 34.

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

Regards, 
fskilnik.

Salsanousi · Answer

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

Answer choice B

MHIKER · Answer

For counting up 15 is the highest and counting down 15 is the lowest. So 15 is counting double.

The total should be 15+20-1= 34

The answer is B.

100mitra · Answer

Correct option B

Radio : 1 item
15th highest = below 14 items are available 
20 lowest = above 19 items are available

Total= 
14 (items with higher price than the radio)+
9(items with lower price than radio)+
1(radio itself)
 =34
Option B

bumpbot · Answer

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

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