GMAT Paper Tests
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
OA B.
At a garage sale, all of the prices of the items sold were
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
The price of the radio was the 15th highest priceAAPL wrote:GMAT Paper Tests
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
OA B.
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@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
A simple drawing does the trick!AAPL wrote:GMAT Paper Tests
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
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7276
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since the radio is the 15th highest and 20th lowest we see that 14 items have a price higher than the radio, and 19 items have a 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.)AAPL wrote:GMAT Paper Tests
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
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews