Data Sufficiency

alex.gellatly wrote:Each of the students in a certain class received a single grade P, F, or I. What percent of the students in the class were females?

1. Of those who received a P, 40percent were females.
2. Of those who received either an F or I, 80 percent where males

Obviously none of the statements are individually sufficient.
Combining both statements together,

• 40% of who received P is female
  20% of who received either F or I is female

As we don't know the number of students who received P, F, or I, we cannot find the total number of females int he class.

Not sufficient

The correct answer is E.

alex.gellatly wrote:Each of the students in a certain class received a single grade P, F, or I. What percent of the students in the class were females?

1. Of those who received a P, 40percent were females.

2. Of those who received either an F or I, 80 percent where males

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

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

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

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent