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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 27 Feb 2013, 04:12
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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%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Feb 2013, 05:51, edited 1 time in total.
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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
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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Re: Attendance at a library for Saturday and Sunday combined   [#permalink] 26 Sep 2017, 02:25
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