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

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
The arithmetic average cost of the three items that Emma purchased fro  [#permalink]

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29 Apr 2018, 08:21
1
00:00

Difficulty:

35% (medium)

Question Stats:

80% (01:15) correct 20% (01:54) wrong based on 25 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. _________________ e-GMAT Representative Joined: 04 Jan 2015 Posts: 2438 Re: The arithmetic average cost of the three items that Emma purchased fro [#permalink] ### Show Tags 29 Apr 2018, 10:42 1 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.

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

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30 Apr 2018, 16:50
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 &nbs [#permalink] 30 Apr 2018, 16:50
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