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I'm unsure if this is the appropriate forum section to post in. Mods, please move if necessary.

One of the requirements for admission to the Lunnville Roller Skating Club is a high degree of skill in roller-skating. The club president has expressed concern that the club may have discriminated against qualified women in its admissions this year. Yet half of the applicants admitted to the club this year were women. This proves that there was no discrimination against qualified women applicants in the club's admissions this year. Which one of the following is an assumption on which the conclusion of the argument depends?

A) Only a few applicants were found to be qualified and were admitted to the club this year.
B) No more than half of all the roller skaters in Lunnville are woman
C) No more than half of all the roller skaters in Lunnville are women
Answer:
D) This year no more than half of the applicants who met all the qualifications for admissions to the club were women
E) This year no more than half of the members of the club committee that makes decisions about applicants' qualifications were men.

My thought process was such the following. Conclusion indicates that there was no discrimination against qualified women this year. Evidence supporting conclusion shows that half of the applicants admitted to the club this year were women. My concern is that shouldnt the answer be "more than half of the applicants were women" rather than "NO more than half of the applicants were women"? If it's anything less than half of the applicants admitted, there is still potentially discrimination within the club. Please, need help to explain. Thanks all

Let's say, for the sake of simplicity, 100 people were admitted this year.

Fact is, 50 women and 50 men were admitted.

Answer says, no more than half of the applicants who met all qualifications for admissions to the club were women.

If say, 1000 qualified people applied, and 500 of them were women (i.e. no more than half), then this would mean %10 admissions rate for both men and women (i.e. no discrimination).

600 women - 400 men? -(i.e. more than half of qualified applicants were women) % 8,33 for admission rate for women, %12,50 admission rate for men - SINCE there are still 50 men and 50 women admitted.

Thus, the discrimination becomes WORSE as the qualified women applicant ratio increases.

Contrapositive is, as qualified women applicant ratio decreases discrimination ceases to be a problem and in fact, for ratios less than 50%, it is reversed;

400 women, 600 men - %12,50 for women, %8,33 for men.

Thats all.

Ah, thanks, now i can see the picture clearer

guess sometimes you really have to draw that out in math to figure out the problem

The denial test is helpful on assumptions - take answer choice D and knock out the "no." If more than half of the qualified applicants who applied were women, but only 50% of the admitted skaters were women, then the claim of no discrimination would seem questionable. For necessary assumptions, knocking out the "no" (or adding it, if it's a positive statement) turns the correct AC into a complete weakener, and thus is TCR. On the other hand, if the AC in question doesn't destroy the argument when negated, it isn't the TCR.