Question: 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.
(2) Of those who received either an F or I, 80 percent were males.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: E

Solution and Explanation:
Approach Solution 1:
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.

Approach Solution 2:
Let T = total number of students in the class

Each received a single grade so T = F + P +I

? % of T = Females

1. of those who received a P, 40% were females
   it doesn't give us the the exact number
2. of those who received either an I or I(I or I ??..may be one of the other two) , 80% were males.
   Still it doesnt give us the number of females

Therefore, Statements (1) and (2) TOGETHER are not sufficient.

Approach Solution 3:
Statement One Alone:

Of those who received a P, 40 percent were females.
This means 0.4p students are females. However, since we know neither the values of p, f, and i nor the percentage of students who received an F or I, statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

This means 20 percent of the students who received either an F or I were females. In other words, 0.2(f + i) students are females. However, since we know neither the values of p, f, and i nor the percentage of students who received a P, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From the two statements, we can say that the percentage of students in the class who were females is:

(0.4p + 0.2(f + i))/(p + f + i) x 100

However, since we don’t know the values of p, f, and i, we can’t determine the numerical value of the expression above. Statements one and two together are still not sufficient

“Each of the students in a certain class received a single grade of P”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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