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30 May 2026, 09:48
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A school bookstore sold only two kinds of planners during orientation week: a basic planner for 8 euros and a deluxe planner for 11 euros. How many planners did the bookstore sell in total?
(1) The average (arithmetic mean) selling price per planner was 9 euros.
(2) The number of basic planners sold was twice the number of deluxe planners sold.
(1) The average (arithmetic mean) selling price per planner was 9 euros.
(2) The number of basic planners sold was twice the number of deluxe planners sold.
30 May 2026, 09:48
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Official Solution:
A school bookstore sold only two kinds of planners during orientation week: a basic planner for 8 euros and a deluxe planner for 11 euros. How many planners did the bookstore sell in total?
(1) The average (arithmetic mean) selling price per planner was 9 euros.
The average price was 9 euros, so
\(\frac{8x + 11y}{x + y} = 9\)
\(8x + 11y = 9x + 9y\)
\(2y = x\)
So (1) tells us only that the number of basic planners sold was twice the number of deluxe planners sold. It does not tell us the total number sold. Not sufficient.
Another way to see the same thing is through distances from the average. The average is 9, which is 1 euro above 8 and 2 euros below 11. Therefore, the number of basic planners sold must be twice the number of 11-euro planners, so that the overall average is pulled closer to 8. But that still does not determine the total number sold. Not sufficient.
(2) The number of basic planners sold was twice the number of deluxe planners sold.
This statement directly tells us that the number of basic planners sold was twice the number of deluxe planners sold. But many totals are still possible. Not sufficient.
(1) + (2) Both statements give the same exact information. So combining them does not help. Not sufficient.
Answer: E
A school bookstore sold only two kinds of planners during orientation week: a basic planner for 8 euros and a deluxe planner for 11 euros. How many planners did the bookstore sell in total?
(1) The average (arithmetic mean) selling price per planner was 9 euros.
The average price was 9 euros, so
\(\frac{8x + 11y}{x + y} = 9\)
\(8x + 11y = 9x + 9y\)
\(2y = x\)
So (1) tells us only that the number of basic planners sold was twice the number of deluxe planners sold. It does not tell us the total number sold. Not sufficient.
Another way to see the same thing is through distances from the average. The average is 9, which is 1 euro above 8 and 2 euros below 11. Therefore, the number of basic planners sold must be twice the number of 11-euro planners, so that the overall average is pulled closer to 8. But that still does not determine the total number sold. Not sufficient.
(2) The number of basic planners sold was twice the number of deluxe planners sold.
This statement directly tells us that the number of basic planners sold was twice the number of deluxe planners sold. But many totals are still possible. Not sufficient.
(1) + (2) Both statements give the same exact information. So combining them does not help. Not sufficient.
Answer: E
