Quote:
The average (arithmetic mean) price of the 3 items that Kate purchased from a clothing store was $50. If there was no sales tax on any item that had a price of less than $80 and 6 percent sales tax on all other items, what was the total sales tax on the 3 items that Kate purchased?
(1) The price of the most expensive item that Kate purchased from the store was $100.
(2) The price of the least expensive item that Kate purchased from the store was $10.
We are given that Kate purchased 3 items from a store at an average price of $50. We are also given that there was no sales tax on an item costing less than $80, and there was a 6% sales tax on all other items. We must determine the total sales tax on the 3 items.
Since average = sum/quantity, we know that sum = average x quantity.
Thus we can say that the sum of the 3 items that Kate purchased is:
50 x 3 = $150
Statement One Alone:The price of the most expensive item that Kate purchased from the store was $100.
Using statement one we can determine that the total cost of the two less expensive items was 150 – 100 = $50. Since the combined price of those cheaper items was under $80, Kate could not have paid any sales tax on those items. She only had to pay sales tax on the $100 item she bought. Thus, her total sales tax was 0.06 x 100 = $6. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:The price of the least expensive item that Kate purchased from the store was $10.
Using statement two we can determine that the total cost of the two more expensive items was 150 – 10 = $140.
However, knowing that the total of the two remaining items is $140 does not sufficiently determine how much tax was paid on all 3 items.
In one scenario, the two remaining items could have cost $70 each and thus no taxes would be paid on those two items or on the $10 item. Thus, total tax = $0.
In another scenario, one of the remaining items could have cost $100 and the other remaining item could have cost $40. Since only one item would have cost more than $80, the total sales tax paid would have been 100 x 0.06 = $6.
Since Kate could have paid $0 or $6 (or some other amounts) in sales tax, statement two is not sufficient to answer the question.
The answer is A.
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