Bunuel wrote:

A student conducts an experiment in biology lab and discovers that the ratio of the number of insects in a given population having characteristic X to the number of insects in the population not having characteristic X is 5:3, and that 3/8 of the insects having characteristic X are male insects. What proportion of the total insect population are male insects having the characteristic X ?

(A) 1/1

(B) 5/8

(C) 6/13

(D) 15/64

(E) 1/5

One key to this problem lies in remembering to sum the parts of a ratio.

Insect characteristic ratio:

\(\frac{X}{NotX}=\frac{5}{3}\)Total parts: 5 + 3 = 8

Insects with X therefore = \(\frac{5}{8}\) of the population.

\(\frac{3}{8}\) OF that population with X, that part, are male.

We need one "part," \(\frac{3}{8}\), of another "part," \(\frac{5}{8}\).

To take a fraction of a fraction, multiply.

\(\frac{3}{8} * \frac{5}{8} = \frac{15}{64}\)

The proportion of the total insect population that are male insects having the characteristic X is \(\frac{15}{64}\).

Check: If there are 64 insects total (denominator), \(\frac{5}{8}\) have X.

\(\frac{5}{8}\) * 60 = 40 insects with X (male and female).

Of those 40 with X, \(\frac{3}{8}\) are male.

\(\frac{3}{8}\) * 40 = 15 males with X

Answer D

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