VJesus12 wrote: ↑Mon Mar 22, 2021 10:08 am
Each of the students in a certain class received a single grade of \(P, F,\) or \(I.\) What percent of the students in the class were females?
(1) Of those who received a \(P, 40\) percent were females.
(1) Of those who received either an \(F\) or \(I, 80\) percent were males.
Answer:
E
Source: GMAT Prep
Target question: What percent of the students in the class were females?
Let's 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 (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- male or female
- received a P or received an F or an I
Since the target question asks for a PERCENT, let's say there are 100 students in total.
So, in order to answer the target question, we need to determine the number of females in the group.
We can set up our matrix as follows:
At this point, we should recognize that statement 1 does not provide any information about the male/female split of students who received an F or an I.
So, statement 1 cannot be sufficient.
Likewise, statement 2 does not provide any information about the male/female split of students who received a P.
So, statement 2 cannot be sufficient.
Statements 1 and 2 combined
Even when we combine the two statements, we realize that we're not told the number of students who received a P and the number of students who received an F or an I
So, there are many possible scenarios that satisfy BOTH statements. Here are two:
Case a: It COULD be the case that 50 students got a P, and 50 students got an F or an I.
In this case, the answer to the target question is
30 percent of the students are female
Case b: It COULD be the case that 90 students got a P, and 10 students got an F or an I.
In this case, the answer to the target question is
38 percent of the students are female
Since we cannot answer the
target question certainty, the combined statements are SUFFICIENT
Answer: E
