Walkabout wrote:
On a company-sponsored cruise, 2/3 of the passengers were company employees and the remaining passengers were their guests. If 3/4 of the company-employee passengers were managers, what was the number of company-employee passengers who were NOT managers?
(1) There were 690 passengers on the cruise.
(2) There were 230 passengers who were guests of the company employees.
Another approach is to use the
Double Matrix Method. 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 passengers, and the two characteristics are:
- company employee or not company employee
- a manager or not a manager
Okay, onto the question...
Target question: What was the number of company-employee passengers who were NOT managers?Given: 2/3 of the passengers were company employees and the remaining passengers were guests. 3/4 of the company-employee passengers were managers.
Let's begin by setting up our diagram to show the two sets of characteristics:
Since we don't know the total number of passengers, let's let x = total number of passengers:
If "
2/3 of the passengers were company employees and the remaining passengers were guests," then 1/3 are guests. This means the sum of the boxes in the left-hand column is (2/3)x and the sum of the boxes in the right-hand column is (1/3)x:
Then we're told that "
3/4 of the company-employee passengers were managers"
So 3/4 of the (2/3)x passenger were managers.
3/4 of (2/3)x = (1/2)x, so (1/2)x passengers were managers:
Since the sum of the two boxes in the left-column must add to (2/3)x, we can conclude that the other box must be (1/6)x, so we can add that here.
IMPORTANT: Since none of the guests were managers, we know that the top-right box contains zero passengers as follows:
Finally, the sum of the two boxes in the right-column must add to (1/3)x, we can conclude that the other box must be (1/3)x, so we can add that here.
Okay, our goal is to determine
the number of company-employee passengers who were NOT managers. In other words, we want to know the number of passengers in the bottom-left box. So, let's place a STAR in this box to remind us of this:
We're now ready to check the statements...
Statement 1: There were 690 passengers on the cruise In other words, x = 690
From this, we can take our diagram and plug in 690 for x:
As we can see, we can determine the number of passengers in every box, which means we can
definitely determine
the number of company-employee passengers who were NOT managersSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: There were 230 passengers who were guests of the company employees.In other words, the boxes in the left-hand column have a sum of 230
If (1/3)x = 230, we can determine the value of x.
Once we know the value of x, we can we can
definitely determine
the number of company-employee passengers who were NOT managersSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
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Two practice questions