each of the students in a certain class...single grade...

[Guest]

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

[Rathna]

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

[RonPurewal]

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

--

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.

--

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.

[lmaura429]

Hi Ron,

Can this be done as an overlapping sets problem?

--------------P-------Not P-------Total
Female---40P------na---------na
Male------na-------80N--------na
Total------P--------N-----------100

Then you see that with both statements, there's no way to solve for F?


Thanks,
Lindsay

[RonPurewal]

Hi Ron,

Can this be done as an overlapping sets problem?

--------------P-------Not P-------Total
Female---40P------na---------na
Male------na-------80N--------na
Total------P--------N-----------100

Then you see that with both statements, there's no way to solve for F?


Thanks,
Lindsay

that's a start.
on the other hand, you've got too many variables here; even if there were a way, you wouldn't discover it if you had "p" and "n" as two different variables.
once you have "p", there's no need for "n", since you have an overall total of 100. therefore, "n" should just be (100 - p).

once you have that, you should actually fill in the rest of the table, and verify that there are indeed multiple possible solutions.
on lots of problems like this one -- just not this one itself -- you'll actually find that these kinds of statements are sufficient. but you have to do the work to find that out.