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Mary purchased 3 theater tickets with an average (arithmetic mean) pri

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Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 05 Jul 2018, 01:37
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Question Stats:

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Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

A. $4
B. $6
C. $8
D. $10
E. $12

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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 05 Jul 2018, 02:13
(3*8 + 1*16)/4 = 40/4 = 10.

Thus, D.

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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 05 Jul 2018, 02:18
Bunuel wrote:
Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

A. $4
B. $6
C. $8
D. $10
E. $12



Here calculations are not much but if it is calculation intensive, we can work on logic..
Average of 3 is 8..
If we add 16-8 =8 extra, this will increase each number by 8/4=2
So new average=8+2=10

D
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 05 Jul 2018, 07:37
Average price of 3 tickets = 8
Total for 3 tickets = 24
Fourth ticket = 16
Avg. price = 16+24/4 = 40/4 =10

Correct answer should be D
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 05 Jul 2018, 07:50
Bunuel wrote:
Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

A. $4
B. $6
C. $8
D. $10
E. $12


\(\frac{3*8 + 16}{4}\)

= 10, Answer must be (D)
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 05 Jul 2018, 16:39
Bunuel wrote:
Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

A. $4
B. $6
C. $8
D. $10
E. $12



Total price of 3 tickets = 3*8 = 24
Price of the 4th tickets = 16

Total price = 40

Average price = 40/ 4 = 10

Thus the best answer is D.
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 06 Jul 2018, 01:48

Solution


Given:
    • The average price of three theater tickets purchased by Mary is $8
    • Now, the price of a fourth theater ticket purchased by Mary is $16

To find:
    • Average price of all the four theater tickets

Approach and Working:
    • Average price of 3 tickets = sum of the prices of three tickets/3 = 8
    • Implies, total price of three tickets = 8 * 3 = 24
    • Average price of four tickets = sum of the prices of four tickets/4
      o Sum of the prices of four tickets = total price of three tickets + price of the fourth ticket = 24 + 16 = 40
    • Thus, average price of four theater tickets purchased by Mary = 40/4 = 10

Hence, the correct answer is option D.

Answer: D
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 06 Jul 2018, 08:21
Bunuel wrote:
Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

A. $4
B. $6
C. $8
D. $10
E. $12



Another way to solve using reasoning.

We have 3 ticket with mean = 8....Any other ticket will increase the mean......Eliminate A, B & C

If we have same number of ticket , the mean will be in the middle between 8 & 16..Hence it should be 12 but we have less tickets with 16....so Eliminate E

We are left with one answer

Answer: D
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri  [#permalink]

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New post 07 Jul 2018, 18:29
Bunuel wrote:
Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

A. $4
B. $6
C. $8
D. $10
E. $12


The average price of the 4 theater tickets is:

(3 x 8 + 16)/4 = 40/4 = 10

Answer: D
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Re: Mary purchased 3 theater tickets with an average (arithmetic mean) pri &nbs [#permalink] 07 Jul 2018, 18:29
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