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The average (arithmetic mean) price of the 3 items

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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The average (arithmetic mean) price of the 3 items

Post Wed Aug 02, 2017 11:17 am
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.

Official Guide question
Answer: A

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GMAT/MBA Expert

Post Wed Aug 02, 2017 6:56 pm
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

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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