Each student was graded A,B orC.What percent of students are female?

Question

In a class, each student received a grade A, B or C. What percentage of students in class are females? 
1) Of those who received B, 40% were females.
2) Of those who received A or C, 60% were males.

ccooley · Accepted Answer

This is an interesting problem, because it plays with your expectations a little bit. My immediate first thought was that the answer would be E. That's because in almost all situations, you'd need to know the percent of students that received a B, versus an A or C. For instance, the answer to this problem would be E: In a class, each student received a grade A, B or C. What percentage of students in class are females? 1) Of those who received B, 40% were females. 2) Of those who received A or C, 50% were males. The only reason this one ends up being 'C' is because the two percents are the same - women make up 40% of each group in the class, so they make up 40% of the whole class, regardless of how big the groups are. And the problem disguises that by giving the 60% figure instead of the 40% one in the second statement - I almost didn't notice. Clever trick!

Chethan92 · Answer

From statement 1:

Of those who received B, 40% were females. So of those who received 60% are males. Ratio of people who received A or C is not given.
Insufficient.

From statement 2:

Of those who received A or C, 60% were males. B ratio is not given.
Insufficient.

Combining both:
A - 60% males , 40% females.
B - 60% males, 40% females.
C - 60% males , 40% females.
Hence sufficient.

C is the answer.

Nums99 · Answer

We need to find the female percentage of students i.e. Number of females / total number of students in the class * 100

St1) B has 40% females 
0.4B are female students 
However no info is given on female from A and C hence this is insufficient

St2) A + C has 60% male thus 40% female
Thus 0.4(A+C) are female students 
But no info on B is given Hence insufficient

Taking both together we know that each student received a grade A, B OR C thus we can say that total number of students are A + B + C 
thus 0.4B + 0.4 ( A + C ) / A + B + C * 100 = 0.4 ( A + B + C ) / A + B + C * 100 = 0.4 * 100 = 40% are females 
Hence both statements together are sufficient

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Each student was graded A,B orC.What percent of students are female?

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Each student was graded A,B orC.What percent of students are female?

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