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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] New post 11 Sep 2012, 04:48
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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.

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

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] 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.

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Question: 37
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Difficulty: 600


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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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] 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] 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] New post 12 Sep 2012, 13:25
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Answer A

Same logic just as above
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Re: The average (arithmetic mean) price of the 3 items that Kate [#permalink] 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] New post 14 Sep 2012, 06:22
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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: The average (arithmetic mean) price of the 3 items that Kate   [#permalink] 14 Sep 2012, 06:22
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