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

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

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05 Feb 2018, 06:09
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15% (low)

Question Stats:

85% (02:03) correct 15% (01:16) wrong based on 33 sessions

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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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05 Feb 2018, 06:32
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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14 Feb 2018, 09:28
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

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

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14 Feb 2018, 09:58
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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14 Feb 2018, 11:01
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.
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A student conducts an experiment in biology lab and discovers that the  [#permalink]

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14 Feb 2018, 11:31
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.

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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15 Feb 2018, 09:18
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.

D.
A student conducts an experiment in biology lab and discovers that the &nbs [#permalink] 15 Feb 2018, 09:18
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