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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 24 Jul 2018, 23:23
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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, 00:41
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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, 06:35
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, 17:38
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  [#permalink]

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New post 28 Aug 2018, 15:13
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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%


It may be useful to use the Double Matrix Method to help us arrange our information. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of theater patrons, and the two characteristics are:
- late or not late
- seated immediately or not seated immediately

So, we get the following:
Image

Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of theater patrons in this population. Let's say there are 100 theater patrons.
Image


5 percent of the theater patrons are late and are seated immediately
The top left box is for theater patrons who are late and are seated immediately. So, 5% of the entire population will be in this box.
Image


30 percent of the patrons who are late are not seated immediately
The patrons referred to here are those who go in the top right box. Unfortunately, we don't know the total number of patrons who are late, so we can't find 30% of that value.
So, let's let x = the total number of patrons who are late.
Image



Now we can deal with this: 30 percent of the patrons who are late are not seated immediately
In other words, 30% of x will go in the top right box.
Image

At this point, we know that the two top boxes must have a sum of x.
So, we can write: 5 + 0.3x = x (now solve)
Rearrange: 5 = 0.7x
Divide: 5/0.7 = x
Or 50/7 = x
Approximate: 7.something = x

Since x represents the total number of patrons who are late, we know that about 7 out of 100 patrons are late.
In other words, about 7% of the patrons are late.

Answer: B

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:

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Re: At the opening night performance of a new play, 5 percent of the theat &nbs [#permalink] 28 Aug 2018, 15:13
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