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Of 30 theater tickets sold, 20 tickets were sold at prices b

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Of 30 theater tickets sold, 20 tickets were sold at prices b [#permalink] New post 23 Feb 2017, 09:10
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Question Stats:

79% (00:38) correct 20% (00:11) wrong based on 48 sessions


Of 30 theater tickets sold, 20 tickets were sold at prices between $10 and $30 each and 10 tickets were sold at prices between $40 and $60 each.

Quantity A
Quantity B
The average (arithmetic mean) of the prices of the 30 tickets
$50


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Of 30 theater tickets sold, 20 tickets were sold at prices b [#permalink] New post 28 Feb 2017, 16:06
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Explanation

Here we have two types of tickets

Type A: 20 tickets @ $10 to $30
Type B: 10 tickets @ $40 to $60


Now for the average of tickets to be maximum the tickets need to be sold at the highest possible price. For type A it is $30 and type B is $60.

Average price of tickets = \(\frac{20 \times $30 + 10 \times $60}{20 +10}= $40\).

Hence Quantity B is greater.


If we select the lower most prices the average price of tickets = \(\frac{20 \times $10 + 10 \times $40}{20 +10}= $20\).

Quantity B is still greater (as expected).

Hence option B is correct.
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Re: Of 30 theater tickets sold, 20 tickets were sold at prices b [#permalink] New post 14 Nov 2018, 10:15
sandy wrote:
Explanation

Here we have two types of tickets

Type A: 20 tickets @ $10 to $30
Type B: 10 tickets @ $40 to $60


Now for the average of tickets to be maximum the tickets need to be sold at the highest possible price. For type A it is $30 and type B is $60.

Average price of tickets = \(\frac{20 \times $30 + 10 \times $60}{20 +10}= $40\).

Hence Quantity B is greater.


If we select the lower most prices the average price of tickets = \(\frac{20 \times $10 + 10 \times $40}{20 +10}= $20\).

Quantity B is still greater (as expected).

Hence option B is correct.


Is it necessary to check for lower range?
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Re: Of 30 theater tickets sold, 20 tickets were sold at prices b [#permalink] New post 14 Nov 2018, 11:50
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As I can see, sandy did.
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Re: Of 30 theater tickets sold, 20 tickets were sold at prices b [#permalink] New post 14 Nov 2018, 13:04
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AE wrote:

Is it necessary to check for lower range?


Not necessary in this case but its a good practice if you are fast enough. It's, what we call, a sanity check. On the test you might commit silly calculation errors, this is a good way to mitigate it.

Also a good practice while in non test situations.
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Re: Of 30 theater tickets sold, 20 tickets were sold at prices b   [#permalink] 14 Nov 2018, 13:04
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