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Attendance at a library for Saturday and Sunday combined

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Attendance at a library for Saturday and Sunday combined [#permalink] New post 27 Feb 2013, 03:12
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Question Stats:

44% (02:32) correct 55% (01:02) wrong based on 56 sessions
Attendance at a library for Saturday and Sunday combined was 50% of the average attendance for the preceding 5 days. The weekend's attendance was approximately what percentage of the attendance for the entire 7-day period?

A. 9%
B. 11%
C. 15%
D. 30%
E. 33%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Feb 2013, 04:51, edited 1 time in total.
Edited the question.
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Re: Attendance at a library for Saturday and Sunday combined w [#permalink] New post 27 Feb 2013, 03:33
Expert's post
emmak wrote:
Attendance at a library for Saturday and Sunday combined was 50% of the average attendance for the preceding 5 days. The weekend's attendance was approximately what percentage of the attendance for the entire 7-day period?

9%

11%

15%

30%

33%


Let the average attendance for the 5 days be 2x. Thus, the total attendance over the weekend was x. The total attendance over the 7 days is : 5*2x+x = 11x.

Thus required percentage :\frac{x}{11x}*100 = 9% approx.
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Re: Attendance at a library for Saturday and Sunday combined w [#permalink] New post 27 Feb 2013, 03:33
emmak wrote:
Attendance at a library for Saturday and Sunday combined was 50% of the average attendance for the preceding 5 days. The weekend's attendance was approximately what percentage of the attendance for the entire 7-day period?

9%

11%

15%

30%

33%

Let no. of attendees during weekdays = 50 (Average of 10 per day)

No. of attendees during weekend = 5

So required ratio = \frac{5}{55}*100 \approx 9%

Answer is A
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Re: Attendance at a library for Saturday and Sunday combined [#permalink] New post 25 Nov 2013, 10:04
Since it's a percentage problem, we can assign nos as per our convenience
Let's assume attendance for Saturday and Sunday combined = 100

"Attendance at a library for Saturday and Sunday combined was 50% of the average attendance for the preceding 5 days"

As per above statement, attendance on Saturday and Sunday combined was 100, then attendance on each weekday - 200

The question asks for percentage of weekend attendance over that of entire week (Attendance of sat and sun/attendance of entire week)*100
Hence, for five days of the week (Mon-Fri) - 200*5 = 1000
Attendance for Sat and Sun = 100
Attendance of entire week = 1000+100 - 1100
Therefore percentage of .... = (100/1100)*100 = 9 (approx)
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Re: Attendance at a library for Saturday and Sunday combined [#permalink] New post 03 Apr 2014, 23:33
Let the 5 days attendance = w

Average = \frac{w}{5}

Weekend attendance = 50% of average

= \frac{50}{100} * \frac{w}{5}

= \frac{w}{10}

Total attendance = w + \frac{w}{10} = \frac{11w}{10}

Weekend attendance percentage

= \frac{\frac{w}{10}}{\frac{11w}{10}} * 100

= 100/11 = 9

Answer =A
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Re: Attendance at a library for Saturday and Sunday combined   [#permalink] 03 Apr 2014, 23:33
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