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At the opening night performance of a new play, 5 percent of the theat

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At the opening night performance of a new play, 5 percent of the theat  [#permalink]

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New post 25 Jul 2018, 00:23
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  85% (hard)

Question Stats:

41% (01:33) correct 59% (01:51) wrong based on 63 sessions

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At the opening night performance of a new play, 5 percent of the theater patrons are late and are seated immediately, but 30 per cent of the patrons who are late are not seated until the end of the first act. Approximately what percent of the theater patrons that evening are late?

(A) 5%
(B) 7%
(C) 35%
(D) 70%
(E) 80%

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At the opening night performance of a new play, 5 percent of the theat  [#permalink]

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New post 25 Jul 2018, 01:41
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Lets 100 be the total number of patrons and X be the number of patrons that are late

30 percent of the patrons who are late are not seated immediately

=> 70 percent of the patrons who are late are seated immediately

=> 70 percent of the patrons who are late are seated immediately = 5 percent of the theater patrons are late and are seated immediately

=> \(\frac{70}{100} * X\) = 5% of total patrons = \(\frac{5}{100} * 100\) = 5

=> X = 7

percent of the theater patrons that evening are late = \(\frac{7}{100} * 100\) = 7%

Hence option B
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Re: At the opening night performance of a new play, 5 percent of the theat  [#permalink]

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New post 01 Aug 2018, 07:35
T = Theater patrons
L = Patrons who are late

If 30% of the patrons are late and did not seat immediately, then 70% of the patrons who are late DID seat immediately. So, The percentage of patrons who are late and seated immediately is 5%*T or 70%*L

then,

5/100T = 70/100L
L/T = 5/70 ≃ 0.071 ≃ 7%

Option B.
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Re: At the opening night performance of a new play, 5 percent of the theat  [#permalink]

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New post 10 Aug 2018, 18:38
Bunuel wrote:
At the opening night performance of a new play, 5 percent of the theater patrons are late and are seated immediately, but 30 per cent of the patrons who are late are not seated until the end of the first act. Approximately what percent of the theater patrons that evening are late?

(A) 5%
(B) 7%
(C) 35%
(D) 70%
(E) 80%


We can let the total number of patrons = X and the number of patrons who are late = L.

Since 30% of the patrons who are late are not seated immediately, 70% of the patrons who are late are seated immediately. Since these patrons are also the 5% of the patrons who are seated immediately. Thus we have:

0.7 L = 0.05 X

L = 0.05/0.7 X= 5/70 X = 1/14 X ≈ 7/100 X

We see that the number of patrons who are late is approximately 7% of the total number of patrons.

Answer: B
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Re: At the opening night performance of a new play, 5 percent of the theat &nbs [#permalink] 10 Aug 2018, 18:38
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