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Re: In a particular professional club, exactly 75 percent of the female me [#permalink]
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Why do we have to assume 50-50% gender participation from both the genders in other solutions. What if there are only 20 females and 80 male, and a total of 100 people in the club. What about this case?

Also, can I get a proper explanation? for concept clarity

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Re: In a particular professional club, exactly 75 percent of the female me [#permalink]
how do we know how many male members are there and how many are female? either could be more which would mean either female engineers are more or the other way.
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In a particular professional club, exactly 75 percent of the female me [#permalink]
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Percent of female members who are mechanical engineers

\(\frac{1}{3}*75\)%\(=\frac{1}{4}=25\)%.


Percent of male members who are engineers = 30%

Since only engineers can be mechanical engineers, the percent of male members who are mechanical engineers ≤ 30% =3/10

Since for both male and female members, the fraction of mechanical engineers among them is less than 1/3, among all members, the fraction of mechanical engineers in the club is definitely less than 1/3.

B>A

Very important note of the author

Note: Had you hurriedly analyzed the questions and based on the information “Exactly 30 percent of the male members are engineers,” concluded that since the information about the fraction of male mechanical engineers is not given, the finite answer to this question is indeterminable, it would have been incorrect.

In most QC questions, we must think of ‘To what extent the maximum or the minimum value of Quantity A or Quantity B can be?’; based on that we can answer many seemingly indeterminable questions. Remember that you need not always get an exact answer to a QC question correctly.
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink]
what if there are 100 females and 1000 males, 75 are engineers, 25 are mechanical engineers. 300 males are engineers, also the proportion of male mechanical engineers is not mentioned, how do we go ahead then,
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