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Operations with Integers Quant Review 2nd Ed #80

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by runningguy » Wed Sep 18, 2013 8:15 am
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

I do not have a clue as to how to start this problem and I cannot understand the explanation given in the answer key. What concept exactly is the GMAT trying to test with this problem?
Last edited by runningguy on Wed Sep 18, 2013 8:39 am, edited 1 time in total.
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by Brent@GMATPrepNow » Wed Sep 18, 2013 8:36 am
runningguy 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
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
Brent Hanneson - Creator of GMATPrepNow.com
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by theCodeToGMAT » Wed Sep 18, 2013 9:26 am
runningguy 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

I do not have a clue as to how to start this problem and I cannot understand the explanation given in the answer key. What concept exactly is the GMAT trying to test with this problem?
GMAT is trying to test the concept of visualization; just try to visualize the scenario and you will get the answer.. Refer the attachment for the solution

Answer is B.

= 14 (elements above Radio) + 19 (elements below Radio) + 1 (Radio itself)
= 34 Elements
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RADIO.jpg
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