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# What percent of the drama club members enrolled at a certain

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Re: What percent of the drama club members enrolled at a certain [#permalink]
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Tricky one. Level 650.

Stmt 1: Tells us about the percentage of female in drama club but does not talk about specific numbers. Not sufficient.
Stmt 2: Tells us about the percentage of male in drama club but does not talk about specific numbers. Not sufficient.

Together also no additional information is provided. Depending on absolute numbers of female or male students, the percentage of female students at drama club will vary.

Bunuel
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Re: What percent of the drama club members enrolled at a certain [#permalink]
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Bunuel
What percent of the drama club members enrolled at a certain school are female students?

(1) Of the female students enrolled at the school, 40 percent are members of the drama club.
(2) Of the male students enrolled at the school, 25 percent are members of the drama club.

$$M+ F= 100$$

very clearly, Both Alone are insufficient. So, take 1+2

let # of females enrolled at school is f, thus$$0.4f$$= # female members at drama school.
let # of males enrolled at school is m, thus, $$0.25m$$ = # male members at drama school

Target question:- $$0.4f/0.4f+0.25m$$ ---> Again, we have no idea what f and m are.

Insufficient. E
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Re: What percent of the drama club members enrolled at a certain [#permalink]
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Abhinandan Dey
Clearly Statement 1 & 2 are individually insufficient.
But if we combine them we get the followings.

40% female are members of drama club means,
Out of 100 female students 40 are in drama club

Accordingly, 2nd statement means,
Out of 100 male students 25 are in drama club.

as it asked the percentage so,
% of female students in drama club is (40/(40+25)) * 100% = 61.5%

So, shouldn't the answer be 61.5%?

Hello abhinandan,

You have assumed numbers to solve the question. This approach, though easy, often leads to errors like the one you have made here.
Let me illustrate:

• You have assumed a total of 100 female students enrolled in the school, out of which 40% (40 female students) are in the drama club.
• Similarly, you assumed a total of 100 male students enrolled in the school, out of which 25% (25 male students) are in drama club.

Now, the issue lies in your assumption of the total number of female and male students. Your numbers indicate that the school will have an equal number of male and female students, but does the question or the statements ever mention that to us? NO!

Now, you may wonder that if you assumed different number of male and female students, would the answer change?

Yes, it surely will! Let me show you:

• Suppose there were a total of 100 female students enrolled in the school just like you assumed, out of which 40% are in the drama club.
• So, we’d have 40 female students in the drama club.
• BUT instead of 100 male students, say we have a total of 200 male students enrolled in the school, out of which 25% are in the drama club.
• So, we’d have 50 male students in the drama club.
• So, total number of students in drama club = 40 + 50 = 90
• Percentage of drama club members that are female students = (Number of female drama club members/ Total number of students in drama club) = 40/90 × 100 = 44.44%

Now, see that this percentage is different than the percentage you calculated for 100 male and 100 female students (61.5%).
Hence, we cannot get a definite answer unless we know the number of or the ratio of male and female students in the school.

Since, this information is not provided in the question or the statements, the 2 statements are insufficient together as well. And the correct choice will be option E.

Hope this helps!

Best Regards,
Ashish Arora
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Re: What percent of the drama club members enrolled at a certain [#permalink]
Clearly Statement 1 & 2 are individually insufficient.
But if we combine them we get the followings.

40% female are members of drama club means,
Out of 100 female students 40 are in drama club

Accordingly, 2nd statement means,
Out of 100 male students 25 are in drama club.

as it asked the percentage so,
% of female students in drama club is (40/(40+25)) * 100% = 61.5%

So, shouldn't the answer be 61.5%?
Re: What percent of the drama club members enrolled at a certain [#permalink]
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