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03 Aug 2026, 10:25
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A neighborhood library purchased 45 paperback copies of a novel at an average price of $16 per copy. It then decided to buy 15 hardcover copies of the same novel as well. Was the average (arithmetic mean) price per copy of all 60 books less than $22?
(1) The total cost of the 15 hardcover copies bought was more than $550
(2) Each hardcover copy cost less than $40.
(1) The total cost of the 15 hardcover copies bought was more than $550
(2) Each hardcover copy cost less than $40.
03 Aug 2026, 10:25
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Official Solution:
A neighborhood library purchased 45 paperback copies of a novel at an average price of $16 per copy. It then decided to buy 15 hardcover copies of the same novel as well. Was the average (arithmetic mean) price per copy of all 60 books less than $22?
Let the total cost of the 15 hardcover copies be \(H\).
The 45 paperback copies cost \(45 * 16 = $720\)
For the average price of all 60 books to be less than $22, the total cost of all 60 books must be less than \(60 * 22 = $1320\)
So we need:
\(720 + H < 1320\)
\(H < 600\)
So the question is really asking:
Is the total cost of the 15 hardcover copies less than \($600\)?
(1) The total cost of the 15 hardcover copies bought was more than $550
This says \(H > 550\). That is not enough to conclude whether \(H < 600\).
Not sufficient.
(2) Each hardcover copy cost less than $40.
Each of the 15 hardcover copies cost less than $40. So:
\(H < 15 * 40 = 600\)
That is exactly what we need.
Sufficient.
Answer: B
A neighborhood library purchased 45 paperback copies of a novel at an average price of $16 per copy. It then decided to buy 15 hardcover copies of the same novel as well. Was the average (arithmetic mean) price per copy of all 60 books less than $22?
Let the total cost of the 15 hardcover copies be \(H\).
The 45 paperback copies cost \(45 * 16 = $720\)
For the average price of all 60 books to be less than $22, the total cost of all 60 books must be less than \(60 * 22 = $1320\)
So we need:
\(720 + H < 1320\)
\(H < 600\)
So the question is really asking:
Is the total cost of the 15 hardcover copies less than \($600\)?
(1) The total cost of the 15 hardcover copies bought was more than $550
This says \(H > 550\). That is not enough to conclude whether \(H < 600\).
Not sufficient.
(2) Each hardcover copy cost less than $40.
Each of the 15 hardcover copies cost less than $40. So:
\(H < 15 * 40 = 600\)
That is exactly what we need.
Sufficient.
Answer: B
