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A student conducts an experiment in biology lab and discovers that the

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New post 05 Feb 2018, 07:09
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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

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Re: A student conducts an experiment in biology lab and discovers that the  [#permalink]

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New post 05 Feb 2018, 07:32
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


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 = \(\frac{15}{64}\)
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New post 14 Feb 2018, 10:28
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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New post 14 Feb 2018, 10:58
These questions are easiest to solve when we use numbers.

Given data: Ratio of insects having characteristic X to not having it is 5:3

Assume the number of insects to be 640.
So, the number of insects having characteristic X is \(\frac{5}{8}*640 = 400\) and those without the characteristic X are 240.

\(\frac{3}{8}\)th of insects having the characteristic X are male, and the number is \(\frac{3}{8}*400 = 150\)

Therefore, the proportion of male insects with characteristic X is \(\frac{150}{640} = \frac{15}{64}\)(Option D)
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Re: A student conducts an experiment in biology lab and discovers that the  [#permalink]

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New post 14 Feb 2018, 12:01
pushpitkc wrote:
These questions are easiest to solve when we use numbers.

Given data: Ratio of insects having characteristic X to not having it is 5:3

Assume the number of insects to be 640.

pushpitkc - absolutely agreed that assigning values is easier.
I would have used 64, cued by 3/8 and 5/8.
It seems in this problem, though, that which number(s) to choose is not very obvious.
What made you choose 640? :-)
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A student conducts an experiment in biology lab and discovers that the  [#permalink]

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New post 14 Feb 2018, 12:31
generis wrote:
pushpitkc wrote:
These questions are easiest to solve when we use numbers.

Given data: Ratio of insects having characteristic X to not having it is 5:3

Assume the number of insects to be 640.

pushpitkc - absolutely agreed that assigning values is easier.
I would have used 64, cued by 3/8 and 5/8.
It seems in this problem, though, that which number(s) to choose is not very obvious.
What made you choose 640? :-)


Nothing in particular. Initially, I arrived at the number 64 only!
But I have always liked working in 10's. So I made the number 640(instead of 64) Helps me calculate faster :-)
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A student conducts an experiment in biology lab and discovers that the  [#permalink]

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New post 15 Feb 2018, 10:18
Let total insect population be x.

Therefore, population with characteristic = 5/8x, population without characteristic = 3/8x.
Also, population with characteristic and is male = (5/8x)*(3/8) = 15/64x.

Hence ratio of this value to total population = (15/64x)/x = 15/64.

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A student conducts an experiment in biology lab and discovers that the &nbs [#permalink] 15 Feb 2018, 10:18
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