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# The average (arithmetic mean) price of the 3 items that Kate

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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]

average of 3 items=50
So 100+10+x/3=50
x=40

Only one item that is more than 80;so Sales tax=.06*100=6
Total Sales Tax=6\$
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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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Bunuel

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.

From stem we know the total value of 3 items = 3 x \$50 = \$150

St 1: Sufficient: If most expensive item is \$100, we have \$ 50 remaining for other two items. So definitely other 2 items are less than \$80.
So Kate has to pay only 6% sales tax for \$100 item.

St 2: Insufficient: If price of least item is \$10, We have \$140 remaining for other 2 items. So 2 items can be a combination of (\$100, \$40) or (\$70, \$70) or (\$80, \$60) etc. So the sales tax will vary depending on the distribution of \$140 with in 2 items.

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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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Total amount of 3 items = 3*50 = \$150

1) Since most expensive item is \$100, then remaining 2 items would have been bought in \$50. Hence we can determine that tax will be applicable only the expensive item which is 6% of 100 = \$6. Sufficient

2) Least expensive item is \$10 which means remaining 2 items might have been bought in \$140 (90,30), (70,70) etc. Cannot determine which need to be taxed. Insufficient.
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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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SOLUTION

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?

It's almost always better to express the average in terms of the sum: so we have that the sum of 3 items Kate purchased is 3*50=\$150.

(1) The price of the most expensive item that Kate purchased from the store was \$100. The sum of the prices of the 2 remaining items is \$150-\$100=\$50. So, each price is less than \$80, which means that Kate paid 6% sales tax only on the most expensive item (6% of \$100). Sufficient.

(2) The price of the least expensive item that Kate purchased from the store was \$10. The sum of the prices of the 2 remaining items is \$150-\$10=\$140. If the 2 remaining prices are \$70 and \$70, then Kate didn't paid sales tax at all, but if the 2 remaining prices are \$100 and \$40, then Kate paid sales tax on \$100 item. Not sufficient.

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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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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.

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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
Bunuel
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.

Practice Questions
Question: 37
Page: 278
Difficulty: 600

Total price of 3 items=3*50=\$150

(1) One out of three items costs \$100
We know the total price of 3 items is \$150
Thus the other two items cost \$50 together.
So there is only 6% sales tax on the \$100 item.

Sufficient

(2) One out of three items costs \$10
Total price is \$150
Thus the other two items cost \$140 together.

Possible cases:
\$140= \$70+\$70 (That means no sales tax)
\$140= \$80+\$60 (That means 6% sales tax on \$80 item).

Insufficient.

A
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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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Hi All,

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

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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]
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