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The arithmetic average cost of the three items that Emma purchased fro

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The arithmetic average cost of the three items that Emma purchased fro [#permalink]

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New post 29 Apr 2018, 09:21
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80% (01:11) correct 20% (01:22) wrong based on 20 sessions

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The arithmetic average cost of the three items that Emma purchased from a grocery store is $25. No sales tax was charged on any item that cost less than $40. A sales tax of 8 percent was charged on any item that cost $40 or more. What is the sales tax on the three items that Emma purchased?

(1) The most costly item that Emma purchased was $50.
(2) The least costly item that Emma purchased was $5.

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Re: The arithmetic average cost of the three items that Emma purchased fro [#permalink]

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Solution



Given:
• Arithmetic average cost of the 3 items purchased by Emma = $25
    o Therefore, total amount spent = $25 * 3 = $75
• Sales tax was charged on any item that cost less than $40
• Sales tax of 8% was charged on any item that cost $40 or more

To find:
• The amount of sales tax charged on the three items purchased by Emma

Analysing Statement 1
• As per the information given in Statement 1, the costliest item purchased by Emma was of $50.
    o As it cost more than $40, the sales tax on this item = ($50 * 0.08) = $4
• Total cost of the remaining 2 items = ($75 - $50) = $25
• As the total cost of remaining 2 items is less than $40, those items can’t have sales tax on them
    o Therefore, the total sales on the 3 items = $4
• Hence, Statement 1 is sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, the least costly item purchased was of $5
    o Therefore, the price of the other 2 items = ($75 - $5) = $70
• Although, the total price of the 2 items is known, no information is provided about their individual price. Depending on the individual prices sales tax can be different. For example:
    o If the prices are $35, and $35, sales tax = 0
    o However, if the prices are $40, and $30 then sales tax = 8% of $40
• Hence, Statement 2 is not sufficient

Hence, the correct answer is Option A.

Answer: A
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Re: The arithmetic average cost of the three items that Emma purchased fro [#permalink]

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New post 30 Apr 2018, 17:50
Option A

\(\frac{(x + y + z)}{3}\) = 25

8% tax > any item that cost $40 or more.

- From (1):

\(\frac{(x + y + 50)}{3}\) = 25

x + y = 25 (less than $40)

> Hence, just one item cost more than $40.

Total sales tax = 50 * \(\frac{8}{100}\) = $4 >>> Sufficient



- From (2):

\(\frac{(5 + y + z)}{3}\) = 25

y + z = 70

We don't know the price of the other 2 items:

- $35/$35 (no tax)
- $50/20 (tax: $4)
- $40/30 (tax: $3,20)

Hence, Not Sufficient


Option A
Re: The arithmetic average cost of the three items that Emma purchased fro   [#permalink] 30 Apr 2018, 17:50
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The arithmetic average cost of the three items that Emma purchased fro

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