yasem77 wrote: ↑

Thu Jun 18, 2009 3:19 am

hello everybody,
can sombody help me wit this task? Actually I thought it´s easy, but I don´t get the answer...

Forty percent of the rats included in an experiment were male rats. If half of the rats died during the experiment and 30 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?

(a) 9/14
(b) 3/4
(c) 9/11
(d) 6/7
(e) 7/8

The answer must be (a) but I don´t know how to get there...

Thanks a lot:-)

One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of rats, and the two characteristics are:
- male or female
- live or die

So, we can set up our matrix as follows


Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.

Since the question provides information with percentages, and since the question asks for a ratio (instead of asking for actual values), we can assign a nice value to the total population of rats in the experiment.
Let's say there are 100 rats.
Since we're told 40% of the rats are male, we know that there are 40 male rats, and the remaining 60 rats must be female.
So, our diagram now looks like this:



Finally, we're told 30% of the rats that died were male rats. This means the remaining 70% of the dead rats must be female.
Since we don't know the total number of rats that died, let's let x = the total number of rats that died
So, 0.3x = the number of dead rats that are male,
And 0.7x = the number of dead rats that are female.


What was the ratio of the death rate among the male rats to the death rate among the female rats?
There are 40 male rats, and 0.3x of them died. So the death rate among the male rats = 0.3x/40
Similarly, there are 60 female rats, and 0.7x of them died. So the death rate among the female rats = 0.7x/60

So, the ratio of the death rate among the male rats to the death rate among the female rats = (0.3x/40)/(0.7x/60)
= (0.3x/40)(60/0.7x)
= 18x/28x
= 18/28
= 9/14

Answer: A