Problem Solving

apoorva.rattan 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:


Aside: To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

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
In other words, 30% of x will go in the top right box.


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, [spoiler]about 7%[/spoiler] of the patrons are late.
Answer: B


Here are some additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Cheers,
Brent

Hi apoorva.rattan,

This type of question involves a sub-group within a larger group. While it can be solved using the Tic-Tac-Toe board, this is not a typical Overlapping Sets question. In this prompt, you MUST pay careful attention to the descriptions, otherwise you will do the math incorrectly.

We're told that there are 2 groups of LATE people. Those who are "seated immediately" and those who are "seated at the end of Act 1." These two sub-groups represent the TOTAL LATE people. The specific information states:

"5% of THEATER PATRONS are late and are seated immediately" - this means 5% of ALL people who show up.
"30% of the PATRONS WHO ARE LATE are not seated until the end of Act 1" - this means 30% of the LATE PEOPLE.

Here is how you can organize all of this information (by TESTing VALUES):

TOTAL PEOPLE = 100

TOTAL LATE PEOPLE = X
5% of ALL PEOPLE are late and seated imeediately = 5
30% of LATE PEOPLE are seated at the end = .3(X)

From this information, we can create an equation:

5 + .3X = X
5 = .7X
50 = 7X
X = about 7

The question asks for the percent of TOTAL PEOPLE who are late: 7/100 = 7%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich