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

Question

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%

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

BrentGMATPrepNow · Accepted Answer

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: 
 https://i.imgur.com/LY43yeR.png

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. 
 https://i.imgur.com/r6BQl4t.png

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. 
 https://i.imgur.com/U4EmVs2.png

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 .
 https://i.imgur.com/JYu3SiM.png

Now we can deal with this:   30 percent of the patrons who are late are not seated immediately  
 https://i.imgur.com/BdlDKbx.png

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:
 https://www.youtube.com/watch?v=jK-tiBrrf04

Nikhil · Answer

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

devlin · Answer

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.

ScottTargetTestPrep · Answer

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

Kinshook · Answer

Given: 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.

Asked: Approximately what percent of the theater patrons that evening are late?

Let the number of theatre patraons be 100 and percentage of theatre patrons who are late be x%

x patrons are late
5 patrons are late and are seated immediately.
.3x are late and are not seated but are not seated until the end of the first act.

.3x + 5 = x
.7x = 5
x = 5/.7 = 7.1%

IMO B

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

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