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

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

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New post 11 Sep 2012, 04:48
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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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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]

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New post 11 Sep 2012, 04:48
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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.

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

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New post 11 Sep 2012, 12:15
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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


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'A' is the answer.
Avg of 3 items is 50. so total cost of all three items will be 150.
as '1' says most expensive item is 100 rs. so other 2 items price sum have 50 (so neither of the two items will have price value more than 80).
so, the sale tax will be on one item which is costing 100Rs.
'2' it says least expensive item is 10. so other two items can be 80&60, 90&50, 100&40, 110&30.. any. so insufficient.
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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink]

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New post 12 Sep 2012, 02:43
C is the answer

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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New post 12 Sep 2012, 03:52
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Bunuel 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.



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.

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

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New post 12 Sep 2012, 15:30
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Answer is A.

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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New post 14 Sep 2012, 06:22
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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.

Answer: A.

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

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New post 09 Aug 2016, 13:51
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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.

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

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New post 01 Apr 2017, 10:57
Bunuel 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.

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

AD

(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).

No unique answer.
Insufficient.

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

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New post 15 Dec 2017, 18:10
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] 15 Dec 2017, 18:10
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