The Official Explanation in
MGMAT CAT Test is :
To solve a population growth question, we can use a population chart to track the growth. The annual growth rate in this question is unknown, so we will represent it as x. For example, if the population doubles each year, x = 2; if it grows by 50% each year, x = 1.5. Each year the population is multiplied by this factor of x.
Time
Population
Now
500
in 1 year
500x
in 2 years
500x2
:
:
in n years
500xn
The question is asking us to find the minimum number of years it will take for the herd to double in number. In other words, we need to find the minimum value of n that would yield a population of 1000 or more.
We can represent this as an inequality:
500xn > 1000
xn > 2
In other words, we need to find what integer value of n would cause xn to be greater than 2. To solve this, we need to know the value of x. Therefore, we can rephrase this question as: “What is x, the annual growth factor of the herd?”
(1) INSUFFICIENT: This tells us that in ten years the following inequality will hold:
500x10 > 5000
x10 > 10
There are an infinite number of growth factors, x, that satisfy this inequality.
For example, x = 1.5 and x = 2 both satisfy this inequality.
If x = 2, the herd of antelope doubles after one year.
If x = 1.5, the herd of antelope will be more than double after two years 500(1.5)(1.5) = 500(2.25).
(2) SUFFICIENT: This will allow us to find the growth factor of the herd. We can represent the growth factor from the statement as y. (NOTE y does not necessarily equal 2x because x is a growth factor. For example, if the herd actually grows at a rate of 10% each year, x = 1.1, but y = 1.2, i.e. 20%)
Time
Population
Now
500
in 1 year
500y
in 2 years
500y2
According to the statement, 500y2 = 980
y2 = 980/500
y2 = 49/25
y = 7/5 OR 1.4 (y can’t be negative because we know the herd is growing)
This means that the hypothetical double rate from the statement represents an annual growth rate of 40%.
The actual growth rate is therefore 20%, so x = 1.2.
The correct answer is B.
So X can take a value of 0.7 or 1.2 right? If I consider y=2x. Why am I not allowed to take y = 2x? Someone plz explain