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30 May 2026, 09:56
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A campus bookstore bought 60 notebooks for a total of 540 euros. All of the notebooks were sold during a three-week orientation period. The notebooks were sold for 14 euros each in week 1, 11 euros each in week 2, and 8 euros each in week 3. Was the number of notebooks sold in week 1 greater than the number sold in week 3?
(1) Fewer than 20 notebooks were sold in week 2.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
(1) Fewer than 20 notebooks were sold in week 2.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
30 May 2026, 09:56
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Official Solution:
A campus bookstore bought 60 notebooks for a total of 540 euros. All of the notebooks were sold during a three-week orientation period. The notebooks were sold for 14 euros each in week 1, 11 euros each in week 2, and 8 euros each in week 3. Was the number of notebooks sold in week 1 greater than the number sold in week 3?
(1) Fewer than 20 notebooks were sold in week 2.
We know:
\(\{week\ 1\} + \{week\ 2\} + \{week\ 3\} = 60\)
But this statement gives information only about \(\{week\ 2\}\). It still leaves many possible values for \(\{week\ 1\}\) and \(\{week\ 3\}\).
Not sufficient.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
The total cost was 540 euros, so the total revenue was less than \(540 + 120 = 660\) euros.
Thus, the average selling price was less than \(\frac{660}{60} = 11\) euros.
Now 11 euros is exactly the price in week 2, and it is exactly halfway between 14 euros in week 1 and 8 euros in week 3.
So, if the overall average selling price is less than 11 euros, then more notebooks must have been sold at 8 euros than at 14 euros, because only then would the average be pulled below 11 euros. Therefore,
\(\{the\ number\ of\ notebooks\ sold\ in\ week\ 3\ at\ 8\ euros\} > \{the\ number\ of\ notebooks\ sold\ in\ week\ 1\ at\ 14\ euros\}\)
So the answer to the question is No. Sufficient.
Answer: B
A campus bookstore bought 60 notebooks for a total of 540 euros. All of the notebooks were sold during a three-week orientation period. The notebooks were sold for 14 euros each in week 1, 11 euros each in week 2, and 8 euros each in week 3. Was the number of notebooks sold in week 1 greater than the number sold in week 3?
(1) Fewer than 20 notebooks were sold in week 2.
We know:
\(\{week\ 1\} + \{week\ 2\} + \{week\ 3\} = 60\)
But this statement gives information only about \(\{week\ 2\}\). It still leaves many possible values for \(\{week\ 1\}\) and \(\{week\ 3\}\).
Not sufficient.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
The total cost was 540 euros, so the total revenue was less than \(540 + 120 = 660\) euros.
Thus, the average selling price was less than \(\frac{660}{60} = 11\) euros.
Now 11 euros is exactly the price in week 2, and it is exactly halfway between 14 euros in week 1 and 8 euros in week 3.
So, if the overall average selling price is less than 11 euros, then more notebooks must have been sold at 8 euros than at 14 euros, because only then would the average be pulled below 11 euros. Therefore,
\(\{the\ number\ of\ notebooks\ sold\ in\ week\ 3\ at\ 8\ euros\} > \{the\ number\ of\ notebooks\ sold\ in\ week\ 1\ at\ 14\ euros\}\)
So the answer to the question is No. Sufficient.
Answer: B
