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Metropolitan Concert Hall was half full on Tuesday night. How many se

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Bunuel
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Metropolitan Concert Hall was half full on Tuesday night. How many se [#permalink] New post   27 Sep 2015, 12:23
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Metropolitan Concert Hall was half full on Tuesday night. How many seats are in the Hall?

(1) If the number of people in the Hall increased by 20% from Tuesday night to Wednesday night, then the Hall would be 60% full on Wednesday night.
(2) If 20 more people showed up on Tuesday night, that would have increased the number of people in the Hall by 4%.


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B
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kunal555
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Re: Metropolitan Concert Hall was half full on Tuesday night. How many se [#permalink] New post   27 Sep 2015, 13:03
Bunuel wrote:
Metropolitan Concert Hall was half full on Tuesday night. How many seats are in the Hall?

(1) If the number of people in the Hall increased by 20% from Tuesday night to Wednesday night, then the Hall would be 60% full on Wednesday night.
(2) If 20 more people showed up on Tuesday night, that would have increased the number of people in the Hall by 4%.


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Statement 1:-
This statement only provides ratios no concrete values. Hence number of seats cannot be determined.
INSUFFICIENT

Statement 2:-
Let x be the number of people who showed up on tuesday.
Then x+20 = 1.04x
or 0.04x=20
or 4x=2000
or x=500
So total seats in the hall will be 2x or 1000
SUFFICIENT

Answer:- B
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Re: Metropolitan Concert Hall was half full on Tuesday night. How many se [#permalink] New post   27 Sep 2015, 19:49
Let the number of seats in the theater be N

On Tuesday the hall was half full
Therefore if T is the number of seats occupied on Tuesday
T = N/2

Statement 1: on Wednesday the number of seats occupied is 20% more than tuesday

= 1.2T

Therefore according to statement 1

1.2T = 0.6(N)
T = N/2
This is same as info in Question stem. Insufficient

Statement 2:

T + 20 = 1.04(T)

This can be solved to find T = 500

From Question stem N = 2T = 1000

Sufficient
Answer = B
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Re: Metropolitan Concert Hall was half full on Tuesday night. How many se [#permalink] New post   29 Sep 2015, 11:17
I believe the answer is B. Please see below for explanation.

T= Total seats

1) From statement we get that if the number of seats on Tuesday increased by 20% that would be the same attendance as in Wednesday night which in turn would be 60% of the total seats meaning

T*0.5*1.20 = T*0.6 --> T*0.6=T*0.6 --> Not Sufficient


2 ) From statement 2 we get that If 20 more people showed up on Tuesday night, that would have increased the number of people in the Hall by 4%. meaning:

T*0.5 + 20 = T*0.5*1.04

From which we can extract a result. Thus statement 2 is Sufficient

Answer B
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Re: Metropolitan Concert Hall was half full on Tuesday night. How many se [#permalink] New post   12 Mar 2018, 02:50
Statement #2: 20 people would be 4% of the audience. Divide by two—10 people would have be 2%; now multiply by five—50 people would have been 10% of the audience; now multiply by ten—500 people would be 100% of the audience on Tuesday night. Since the concert hall was half full, there must be 1000 seats in total. This piece of information allows us to solve for the answer to the prompt question. This statement, alone and by itself, is sufficient.

First statement insufficient, second sufficient. Answer = B
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Re: Metropolitan Concert Hall was half full on Tuesday night. How many se [#permalink]
12 Mar 2018, 02:50
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