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# On a certain week, 1000 visitors chose one of weekdays days from Monda

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Joined: 02 Sep 2009
Posts: 55668
On a certain week, 1000 visitors chose one of weekdays days from Monda  [#permalink]

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24 Oct 2018, 00:35
00:00

Difficulty:

85% (hard)

Question Stats:

44% (02:29) correct 56% (02:41) wrong based on 45 sessions

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On a certain week, 1000 visitors chose one of weekdays days from Monday through Sunday to visit a pagoda. If twice as many visitors chose Monday than Tuesday, did at least 100 visitors choose Sunday?

(1) None of the weekdays was chosen by more than 150 visitors.
(2) None of the weekdays was chosen by fewer than 75 visitors.

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Re: On a certain week, 1000 visitors chose one of weekdays days from Monda  [#permalink]

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24 Oct 2018, 02:26
Bunuel wrote:
On a certain week, 1000 visitors chose one of weekdays days from Monday through Sunday to visit a pagoda. If twice as many visitors chose Monday than Tuesday, did at least 100 visitors choose Sunday?

(1) None of the weekdays was chosen by more than 150 visitors.
(2) None of the weekdays was chosen by fewer than 75 visitors.

Question: Is Sunday ≥ 100?

Given: If Tuesday = x, then Monday = 2x

Statement 1: None of the weekdays was chosen by more than 150 visitors.

i.e. Sunday visitors will be least when total visitors on other days are maximum i.e. 150

i.e. Maximum Visitors on 6 days from Monday to Saturday = 150*6 = 900

i.e. Minimum Visitors on Sunday = 1000 - 900 = 100

SUFFICIENT

Statement 2: None of the weekdays was chosen by fewer than 75 visitors

NOT SUFFICIENT

Answer: Option A
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Re: On a certain week, 1000 visitors chose one of weekdays days from Monda  [#permalink]

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26 Oct 2018, 08:37
Bunuel wrote:
On a certain week, 1000 visitors chose one of weekdays days from Monday through Sunday to visit a pagoda. If twice as many visitors chose Monday than Tuesday, did at least 100 visitors choose Sunday?

(1) None of the weekdays was chosen by more than 150 visitors.
(2) None of the weekdays was chosen by fewer than 75 visitors.

I think there is a flaw in the question.

From the question:
Total visitors = 1000
Monday Visitors = 2 * Tuesday Visitors

(1) number of Daily visitors < 150, If all days have the maximum number of visitors of 150 and to respect the relation between the number of visitors on Monday and Tuesday, we would have:
Sun, Mon, Wed, Thu, Fri e Sat = 150 (6 * 150 = 900 visitors)
Tuesday = 75 visitors

Total = 975 visitors (and NOT 1000 visitors!)

It does not respect the total number of visitors

(2) number of Daily visitors > 75, If all days have the minimum number of visitors of 75 and to respect the relation between the number of visitors in Monday and Tuesdays, we would have:
Sun, Tue, Wed, Thu, Fri e Sat = 75 (6 * 75 = 450 visitors)
Monday = 150 visitors

Total = 600 visitors : 400 visitors left to distribute on the others days, but we don't have any more information to distribute these visitors.

NOT SUFFICIENT

Both together we have the same problem from (1): It does not respect the total number of visitors
Re: On a certain week, 1000 visitors chose one of weekdays days from Monda   [#permalink] 26 Oct 2018, 08:37
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# On a certain week, 1000 visitors chose one of weekdays days from Monda

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