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In a particular professional club, exactly 75 percent of the female me

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In a particular professional club, exactly 75 percent of the female me [#permalink] New post   10 Sep 2023, 10:00
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In a particular professional club, exactly 75 percent of the female members are engineers, and, of them, 1/3 are mechanical engineers. Exactly 30 percent of the male members are engineers. It is known that, only those who are engineers can be mechanical engineers.


Quantity A
Quantity B
Fraction of the members who are mechanical engineers in the club
\(\frac{1}{3}\)



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



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B
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jiayou111
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   24 Sep 2023, 18:05
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Since there's no given numbers, pretend that the total number of members is 200. There are 100 male members and 100 female members.

If there are 100 female members, 75 are engineers (100 * 0.75). Of the 75 engineers, 1/3 are mechanical engineers. 75 * 1/3 = 25. There are 25 female mechanical engineers.

There are 100 male members, 30% are engineers, so 100 * 0. 3 = 30 male engineers. In the scenario that maximizes the number of possible mechanical engineers, say all 30 engineers are also mechanical engineers.

25 + 30 = 55

55/ 200 < 1/3

This means that even in the maximum scenario where all male engineers are mechanical engineers, it is still less than 1/3. Therefore, in all scenarios of male mechanical engineers, the ratio of mechanical engineers to the total organization population will be less than 1/3. Choice B is the answer.
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Ayammali602
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   13 Nov 2023, 19:25
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Assum we have 100 female and 100 male with total 200.

Females were 75 eng. and 75/3 = 1/3 M.eng and Males were 30 Eng. so their M.Eng will be a max. less than 1/3-.
so , the total m.eng female + male as maxmiam will less than 1/3 of 200.
Ans: B
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dakshdhull
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   04 Mar 2024, 02:20
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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

Thanks

Sincerely
Daksh
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steveharvi
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   09 Apr 2024, 02:44
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] New post   09 Apr 2024, 03:18
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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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steveharvi
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   10 Apr 2024, 10:55
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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pinkpanthermath
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   19 May 2025, 07:20
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Let the total number of people be 100

75 of them are female eng.

1/3 of 75= 25 are mech eng

Now, since 75 are females, 25 must be males.

out of those 25, 0.3 are eng.

Even if we assume all male eng are mech eng then it'll be 7.5 ~ 8

frac of total mech eng = 32/100 ~ 0.32
Which is smaller than 1/3 ~ 0.3333


However, our answer would likely be less than 0.32 since we have assumed all male eng to be mech eng. But that's the upper bound, so it works.
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lmd9712
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink] New post   17 Aug 2026, 20:44
I got this wrong and had the same thought as many others -- how can we say if we don't know the # of male engineers? I found it helpful and more intuitive to think of this as a weighted average problem -- at MOST, the men will be 30% ME. The women will be 25% ME. So no matter how many men and women, the number of ME as % of total must be between 30% and 25%. 1/3 is 33.3333% so it will always be greater.
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Re: In a particular professional club, exactly 75 percent of the female me [#permalink]
17 Aug 2026, 20:44
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