So this problem is weird — because
both B and E must be correct.
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B can be proved by just a couple of observations:
• The
overall acceptance rate is a
WEIGHTED AVERAGE of the acceptance rates for the
individual categories.
• Like other weighted averages, this one will depend on the
proportions/fractions/percentages of films in each of the two categories.
HIGHER % of films in DRAMA = LOWER weighted-average acceptance rate.
• The weighted average is lower for foreign films, so, accordingly, a higher % of foreign films must have been accepted into the drama category. Choice B is thus proved.
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This is where it gets innnnnnnteresting.
Once we've proved the result above... we can now go on to show that
choice E must be true, too!Let's imagine, hypothetically, that choice E is FALSE. I.e., 50% or fewer of the foreign films were dramas.
Remember (choice B) that an even LOWER percentage of
domestic films are dramas.
Therefore,
in this hypothetical case...
... ≤ 50% of foreign films are dramas;
... < 50% of domestic films are dramas.
Together, that's definitely a MINORITY of ALL the films submitted.
This is a problem, because we're told that the drama category
ALWAYS receives more submissions than does the comedy category.
"Always" is not a figure of speech, nor is it inexact — it means exactly what it says. So,
this hypothetical is impossible, because it violates the "ALWAYS" statement.
Since it's impossible for 50% or fewer of the foreign films to be dramas, then,
it is thus PROVED that MORE than 50% of the foreign films are dramas.
That's choice E.
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Oh well ahah. I just hope this problem wasn't ever a non-experimental problem on the real exam.
(There are only 2 other GMAC quant problems I've ever seen for which the OA was actually incorrect — so, you shouldn't let this one shake your confidence in the validity of the test overall.)
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