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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:26) correct
39%
(01:59)
wrong
based on 396
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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%
(A) 5%
(B) 7%
(C) 35%
(D) 70%
(E) 80%
Updated on: 05 May 2021, 07:35
Originally posted by BrentGMATPrepNow on 28 Aug 2018, 16:13.
Last edited by BrentGMATPrepNow on 05 May 2021, 07:35, edited 1 time in total.
Last edited by BrentGMATPrepNow on 05 May 2021, 07:35, edited 1 time in total.
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Bunuel
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:
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.
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.
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.
Now we can deal with this: 30 percent of the patrons who are late are not seated immediately
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:
General Discussion
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
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
