Lecture Hall Ratio

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In a lecture hall, what is the ratio of the number of women to the number of men?

(1) There are twice as many women as men in the lecture hall.

(2) The number of men is of the number of men and women in the lecture hall.

Review: Lecture Hall Ratio




Explanation

We have a simple question: we need the ratio of women to men. When we hear "ratio," we convert it in our mind to a fraction with unit labels. So we need to fill in the question marks in this expression:



On to the data statements, separately first. Statement (1) should be sufficient. If the number of men is M, the number of women is 2M. Plugging those values into the fraction, we see the M's cancel and the ratio is 2 women to 1 man. Sufficient. Statement (2) is formulated in terms of the total, but it looks promising. Indeed, we don't want to use Statement (1) as data, but we can see that Statement (2) is saying the same thing: if there are M men and 2M women, then there are 3M men and women together, and men will be a third of the total. So Statement (2) is sufficient.

The correct answer is (D).


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