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DS Percent of females

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by neeti2711 » Sun Mar 03, 2013 2:48 am
Each of the students in a certain class received 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 F or I, 80% were females
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Source: — Data Sufficiency |
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by aditya8062 » Sun Mar 03, 2013 2:54 am
my take wud be E .will put my reasoning if u plz confirm the answer
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by Anurag@Gurome » Sun Mar 03, 2013 8:51 am
neeti2711 wrote:Each of the students in a certain class received 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 F or I, 80% were females
As neither the question nor the statements tell us anything about the percentage of males, there is a chance that both statements together also will not be sufficient. Let us check that scenario first with some numbers.

Example 1:
  • P = F = I = 100 --> Total = 300
    Total number of female = 40% of P + 80% of (F + I) = 40 + 160 = 200
    Hence, required percentage = 100*(200/300) ≈ 67%
Example 2:
  • P = 100, F = I = 200 --> Total = 500
    Total number of female = 40% of P + 80% of (F + I) = 40 + 320 = 360
    Hence, required percentage = 100*(360/500) = 72%
Both of the above examples satisfy both the statements, but the percentage of females are different.
Hence, both statements together is also not sufficient.

The correct answer is E.
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by GMATGuruNY » Mon Mar 04, 2013 8:57 am
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
When the statements are combined:
Of those who received a P, 40% are female.
Of those who received an F or I, 20% are female.

Case 1: P=10, F+I=90
Percent of the 100 students who are female = .4(10) + .2(90) = 22.

Case 2: P=90, F+I=10
Percent of the 100 students who are female = .4(90) + .2(10) = 38.

Since different percentages are possible, INSUFFICIENT.

The correct answer is E.
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