Each of the students in a certain class received a single gr

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ktrout2020: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Wed Oct 30, 2019 1:10 pm

by ktrout2020 » Sun Nov 03, 2019 11:00 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.

Source: GMATPrep practice test

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Source: Beat The GMAT — Data Sufficiency | Sun Nov 03, 2019 11:00 am

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by GMATGuruNY » Mon Nov 04, 2019 4:00 am

ktrout2020 wrote: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.

Source: GMATPrep practice test

Statement 1: Of those who received P, 40% were females.
Statement 2: Of those who received F or I, 80% were males -- implying that 20% were females.

Try EXTREMES.
Let the total number of students = 100.

Case 1: Total P = 90 and Total F or I = 10.
Percent women = .4(90) + .2(10) = 38%.

Case 2: Total P = 10 and Total F or I = 90.
Percent women = .4(10) + .2(90) = 22%.

Since different percentages are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.

This is a MIXTURE problem.
The percentage of women who receive P (40%) is combined with the percentage of women who receive F or I (20%) to form a mixture: the entire class.
The percentage of women in the mixture can be ANY VALUE between 20% and 40%.

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by Brent@GMATPrepNow » Mon Nov 04, 2019 5:49 am

ktrout2020 wrote: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.

Source: GMATPrep practice test

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.

Brent Hanneson - Creator of GMATPrepNow.com

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