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05 Feb 2018, 07:09
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D
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Difficulty:
5%
(low)
Question Stats:
87% (01:57) correct
13%
(02:20)
wrong
based on 158
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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
(A) 1/1
(B) 5/8
(C) 6/13
(D) 15/64
(E) 1/5
05 Feb 2018, 07:32
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Bunuel
Let #Insect with Characteristic X be Ic and #Insect without Characteristic X be In,
Then given , \(\frac{Ic}{In}=\frac{5}{3}\)
So let 5x = #Insect with Characteristic X & 3x = #Insect without Characteristic X
Total Population = 8x
Now given that \(\frac{3}{8}Ic=#Male Insect\) ==> \(\frac{3}{8}*5x\) ==> #male insect = \(\frac{15}{8}*x\)
So asked ==> #Male Insect/Total Insect = \(\frac{15}{64}\)
14 Feb 2018, 10:28
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Bunuel
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
