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06 Mar 2025, 01:30
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E
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Difficulty:
25%
(medium)
Question Stats:
85% (01:10) correct
15%
(02:02)
wrong
based on 59
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If Matilda bought a 50 items for a total of $50,000, what was the cost of the least expensive item?
(1) The lowest priced item was 1/3 the cost of the highest priced item.
(2) The average (arithmetic mean) price paid was $100.
(1) The lowest priced item was 1/3 the cost of the highest priced item.
(2) The average (arithmetic mean) price paid was $100.
06 Mar 2025, 03:30
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We are given the following situation: Matilda bought 50 items for a total of $50,000, and we need to find the cost of the least expensive item.
Statement (1): The lowest priced item was 1/3 the cost of the highest priced item.
Let the price of the least expensive item be L, the price of the most expensive item be H.
According to this statement:
L = 1/3 H
This gives us a relationship between the prices of the least and most expensive items. However, this statement does not provide enough information about the other items or their individual prices. There could still be multiple ways to distribute the total $50,000 among the 50 items. Therefore, Statement (1) alone is not sufficient
Statement (2): The average price paid was $100.
The average price paid for the 50 items is given as $100. Since the total cost of all 50 items is $50,000, the average price is:
50,000/50 =100
This statement tells us that the average price of the items is $100, but it does not provide specific information about the distribution of individual item prices, including the least expensive item. Statement (2) alone is also not sufficient
Combining Statements (1) and (2):
From Statement (2), we know the total cost of all 50 items is $50,000, and the average price is $100.
From Statement (1), we know the relationship between the least expensive item
L and most expensive item H.
The total cost of the 50 items is $50,000, so the sum of all item prices must be $50,000.
However, even with both statements, the information about the other 48 items (which are neither the least expensive nor the most expensive) is still insufficient to uniquely determine the value of L.
Thus, the two statements together are not sufficient to determine the cost of the least expensive item.
Conclusion:
The correct answer is (E): The statements together are not sufficient to answer the question.
Statement (1): The lowest priced item was 1/3 the cost of the highest priced item.
Let the price of the least expensive item be L, the price of the most expensive item be H.
According to this statement:
L = 1/3 H
This gives us a relationship between the prices of the least and most expensive items. However, this statement does not provide enough information about the other items or their individual prices. There could still be multiple ways to distribute the total $50,000 among the 50 items. Therefore, Statement (1) alone is not sufficient
Statement (2): The average price paid was $100.
The average price paid for the 50 items is given as $100. Since the total cost of all 50 items is $50,000, the average price is:
50,000/50 =100
This statement tells us that the average price of the items is $100, but it does not provide specific information about the distribution of individual item prices, including the least expensive item. Statement (2) alone is also not sufficient
Combining Statements (1) and (2):
From Statement (2), we know the total cost of all 50 items is $50,000, and the average price is $100.
From Statement (1), we know the relationship between the least expensive item
L and most expensive item H.
The total cost of the 50 items is $50,000, so the sum of all item prices must be $50,000.
However, even with both statements, the information about the other 48 items (which are neither the least expensive nor the most expensive) is still insufficient to uniquely determine the value of L.
Thus, the two statements together are not sufficient to determine the cost of the least expensive item.
Conclusion:
The correct answer is (E): The statements together are not sufficient to answer the question.
