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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]

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New post Updated on: 27 Feb 2013, 05:51
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Question Stats:

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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%

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Originally posted by emmak on 27 Feb 2013, 04:12.
Last edited by Bunuel on 27 Feb 2013, 05:51, edited 1 time in total.
Edited the question.
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Re: Attendance at a library for Saturday and Sunday combined w  [#permalink]

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New post 27 Feb 2013, 04:33
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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]

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New post 27 Feb 2013, 04:33
1
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]

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New post 25 Nov 2013, 11:04
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]

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New post 04 Apr 2014, 00:33
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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]

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New post 04 Dec 2015, 19:08
I picked numbers..
suppose the average attendance during M-F is 20/day. avg is 20. during weekend, only 10.
we thus have 110 people in total, out of which 10 during weekend.
10/110 = 1/11 which is aprox. 0.09
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Re: Attendance at a library for Saturday and Sunday combined  [#permalink]

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New post 26 Sep 2017, 02:25
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?

A. 9%
B. 11%
C. 15%
D. 30%
E. 33%


Let the days of week be numbered as xn
So, x6+x7 =50% of (x1+......+x5)/5 = (x1+......+x5)/10
-> (x1+......+x5) = 10*(x6+x7)

So, (x1+x2+.....+x6+x7) = 10*(x6+x7) + (x6+x7) = 11*(x6+x7)

So percentage = (x6+x7)/[11*(x6+x7)] *100 = 9.09

Answer A
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Attendance at a library for Saturday and Sunday combined  [#permalink]

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New post 13 Jan 2018, 08:40
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?

A. 9%
B. 11%
C. 15%
D. 30%
E. 33%



The easiest way to go about answering the question is picking number.

Assume the average attendance of the week to be 50, meaning that
each day of the week, the library had an attendance of 50. Since, the
attendance of the weekend combined was 50% of the preceeding 5
days, it must be 25.

Total attendance in a 7 year period is \(50*5 + 25 = 275\)
27.5 will be 10%, so 25 should be less than 10%, the only answer option is(Option A- 9%)
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Attendance at a library for Saturday and Sunday combined   [#permalink] 13 Jan 2018, 08:40
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