The average (arithmetic mean) price of the 3 items

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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.

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Answer: A

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by [email protected] » Wed Aug 02, 2017 6:56 pm

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Hi jjjinapinch,

We're told that the average price of the 3 items purchased was $50, there was NO sales tax on any item that had a price of LESS than $80 and a 6 percent sales tax on all other items (meaning those items priced $80 or higher). We're asked for the TOTAL TAX on the 3 items. This question can be solved by TESTing VALUES.

To start, since the AVERAGE price of the 3 items (pre-tax) was $50, the TOTAL spent was...
(Total)/3 = $50
Total spent (pre-tax) = $150

Since only the items that cost $80 (or more) were taxed, no more than one of the three items could possibly have been taxed - and it's possible that none of the 3 items were taxed.

1) The price of the most expensive item that Kate purchased from the store was $100.

Fact 1 gives us the price of the MOST expensive item, so we can calculate the tax on THAT item (6% of $100 = $6). The remaining two items cost a total of $50, so neither of them would have been taxed. Thus, the answer to the question is $6.
Fact 1 is SUFFICIENT

2) The price of the least expensive item that Kate purchased from the store was $10.

IF....
the 3 items cost: $10, $70, $70, then the total tax would be $0
the 3 items cost: $10, $40, $100, then the total tax would be $6
Fact 2 is INSUFFICIENT

Final Answer: A

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by Jeff@TargetTestPrep » Fri Aug 03, 2018 2:09 pm

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jjjinapinch wrote: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.

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.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
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