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% were females
2. of those who received either an I or F, 80% were males.







one way you could do it: number picking. just try different numbers of P's and I's/F's, and see whether the answer is invariant or whether it changes. if it changes at all, then the data are insufficient.
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you could also do it by realizing that this is a WEIGHTED AVERAGE of 40% (the percentage of p's that are female) and 20% (the percentage of f/i's that are female). like any other weighted average, this one depends on the relative quantities of its components (here, p's versus f/i's), quantities that are not given in either of the two statements.
conceptually, if there are huge numbers of p's and negligible numbers of f/i's, then the percentage of females will be very close to 40%. conversely, if there are huge numbers of f/i's and very few p's, then the percentage will be very close to 20%.

in fact, there's nothing prohibiting the consideration of the two most extreme cases possible:
* ALL grades are p's --> 40% female
* ALL grades are f/i's --> 20% female
these situations are both allowed under the given conditions, so, insufficient.


Ans - E