can someone explain this soln?

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 I, 80% were males.

ans: e

thanx

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 doesnt 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

so E

CAVEAT LECTOR: i'm going to assume that "either I or I" is supposed to say "either F or I". proceed accordingly.

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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.

* let's try 100 p's and 100 f/i's
among the 100 p's, there are 60 males and 40 females.
among the 100 f/i's, there are 80 males and 20 females.
so 60 out of 200, or 30%, are female.

* let's try 1000 p's and 100 f/i's
among the 1000 p's, there are 600 males and 400 females.
among the 100 f/i's, there are 80 males and 20 females.
so 420 out of 1100 are female. this is a weird percentage, but it's clearly not 30% (which would be 330 out of 1100), so, 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.