144144 wrote:
A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people surveyed said that they buy neither product P nor product Q?
(1) 1/3 of the people surveyed said that they buy product P but not product Q.
(2) 1/2 of the people surveyed said that they buy product Q.
This is a great candidate for a technique called the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- buy product Q or not buy product Q
- buy product P or not buy product P
When I scan the two statements I see that they mention
1/3 of the people surveyed and
1/2 of the people surveyed. I also see that the target question asks us to find a
fraction of the people surveyed (not the actual number). So, let's pick a nice number that works well with
1/3 and
1/2.
Let's say there
12 people were surveyed.
So, we'll start by setting up our diagram like this:
We want to find the fraction of the people surveyed said that they neither buy product P nor product Q. So, to answer this question, we need to know the number of people in the bottom right box (where the happy face is).
We're now ready to check the statements.
Statement 1: 1/3 of the people surveyed said that they buy product P but not product Q.
1/3 of 12 = 4. So, 4 people buy product P but not product Q.
Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
No.
Statement 1 is NOT SUFFICIENT
Statement 2: 1/2 of the people surveyed said that they buy product Q.
So, 6 people buy product Q, which means 6 people do not buy product Q
Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
No.
Statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
We get:
Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
YES.
Since the two boxed in the right-hand column must add to 6, the bottom right box must have
2 people, which means
2/12 people said that they neither buy product P nor product Q. Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer:
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