In a certain survey, 1,200 people were asked which they

Question

In a certain survey, 1,200 people were asked which they preferred, comedic films or dramatic films. If each respondent expressed a preference for one or the other, how many female respondents surveyed preferred comedic films?

(1) Seventy-four percent of the females preferred dramatic films.
(2) Sixty-four percent of the respondents preferred dramatic films.

gmat1220 · Answer

how many female respondents surveyed preferred comedic films ? or this can be rephrased can - Can we dissect female population according to their taste of dramatic and comedic films?

1) Insufficient.

m + f = 12000
The fact that 0.72f preferred dramatic films does not allows us to make an equation.

2) Insufficient.

The total number who preferred dramatic films = 0.64 * 12000
does not allows us to make an equation.

1) + 2) Does not answer the question. We don't know how many males preferred the dramatic films. And we don't know the overlaps. Answer E

subhashghosh · Answer

Total = M + F = 1200

(1) says, 74% of females = dramatic films

=> 26% of females = Comedy

0.26F = Comedy

But, we don't know the # of females, so insufficient

(2) says, 64% of respondents = dramatic

=> 36% of people = Comedy

0.36(1200) = Comedy

But we don't know the Male-Female breakup, so insufficient.

(1) and (2) together :

0.26F + x/100M = 0.36 * 1200 (x is %age of males who like comedy)

We don't know x here.

Answer - E

subhashghosh · Answer

This question has a discrepancy:

As per (2) we can have 0.36(M+F) = Comedy;

=> 0.36M + 0.36F = Comedy

but as per (1) we have 0.26F = Comedy.

So the overlapping number is obscure, and again, this makes the answer E.

ravsg · Answer

Both 1 and 2 don't provide info. So E.

beyondgmatscore · Answer

I don't think we can conclude that there is a discrepancy here.

The Comedy in your first equation (colored red above) refers to Total number of people preferring Comedy

Whereas, Comedy in your second equation (colored blue above) refers to total number of females preferring Comedy.

So, both statements can be true.

For example, if there were 1000 males and 200 females, then 1st equation just says that 36% of 1200 prefer comedy and that comes to a total of 432 people - which is the same total if 36% of males as well as 36% of females preferred Comedy, but that's not the only combination that can give us 432, as we see below.

The second equation says that 26% of 200 females prefer comedy and that comes to a total of 52 females.

So, number of males preferring comedy is 432 - 52 = 380, and hence percentage of males preferring comedy is 38%. So, for this male female breakup, total 26% can prefer comedy if 38% males and 26% females prefer comedy.

Of course, the answer still is E.

KarishmaB · Answer

I love to tell people that they should spend quite a bit of time getting comfortable with weighted averages because it is a concept that is very useful in many questions. This is a perfect example of that. Normally you wouldn't think of using weighted averages here but the moment I read the question, I knew the answer is E. 
The reason - I like to think in terms of averages.

Let me explain:

Females preferring dramatic films = 74%
Total people preferring dramatic films (i.e. the weighted average) = 64%
Males preferring the dramatic films - unknown
Ratio of males:females - unknown
Since there are these two unknowns, we cannot find the ratio of males:females and hence cannot find the number of females and hence cannot find the number of females who prefer comedic films. 
Mind you, this takes a moment to flash when you just think of the scale and imagine the 64% in the center and 74% on right side and the empty left side and empty top...

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