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03 Oct 2022, 01:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
62% (01:14) correct
38%
(01:17)
wrong
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A newly released book includes hardback and paperback. If the sales price for the hardback is $20, and the sales price for the paperback is $15, what is the average price for all of the books sold during a certain day?
(1) The ratio of the number of the hardback sold to the number of paperback sold is 5 to 3.
(2) A total of 160 books were sold during the day.
(1) The ratio of the number of the hardback sold to the number of paperback sold is 5 to 3.
(2) A total of 160 books were sold during the day.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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03 Oct 2022, 05:23
Kudos
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OA:A
Avg price= ((weights of quantity of hardcover*price of hardcover)+(weights of quantity of paperback*price of paperback))/Total weight
So here the key is that you don't need to know the actual quantity of books sold. You are good to go if you just have the weights
Looking at st 2 alone : Total books are given but distribution or weights aren't given making the this statement insufficient
Looking at st 1 alone: Weights are given and this is suffice to find the avg price
Avg price= ((weights of quantity of hardcover*price of hardcover)+(weights of quantity of paperback*price of paperback))/Total weight
So here the key is that you don't need to know the actual quantity of books sold. You are good to go if you just have the weights
Looking at st 2 alone : Total books are given but distribution or weights aren't given making the this statement insufficient
Looking at st 1 alone: Weights are given and this is suffice to find the avg price
03 Oct 2022, 08:21
Kudos
Bookmarks
Bunuel
Solution:
Pre Analysis:
- Sale price of hardback \(=$20\)
- Sale price of paperback \(=$15\)
- We are asked the average sale price of all the books sold during a day
Statement 1: The ratio of the number of the hardback sold to the number of paperbacks sold is 5 to 3
- Let the number of hardback to paper sold be \(5x\) and \(3x\) respectively
- Sale price of \(5x\) hardbacks \(=20\times 5x=100x\)
- Sale price of \(3x\) paperbacks \(=15\times 3x=45x\)
- Average sale price =\(\frac{\text{Total sale pirce}}{\text{Total books sold}}=\frac{100x+45x}{5x+3x}=\frac{145x}{8x}=\frac{145}{8}\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: A total of 160 books were sold during the day
- This information gives us no information on the number of paperback and hardback sold
- Average sale price \(=\frac{\text{Total sale pirce}}{\text{Total books sold}}=\frac{\text{Total sale pirce}}{160}\)
- Thus, statement t2 alone is not sufficient
Hence the right answer is Option A
