Number property-MAN Flash card

[rishijhawar]

A group of rabbits multiplies at a constant rate. By what factor does its population increase every day?
(1) The population grows from 200 to 5,000 in one week.
[spoiler]Though the question is testing suffiency of (1) above, my question is how to arrive at a final answer
if it were a PSolving sum. I used GP and reached till r^(n-1)=50. Thanks[/spoiler]

[sandeeptalla450]

Assume constant rate as r. The populations of that week can be written as:

200, 200r, 200*(r^2), ...,200*(r^6)

We know that the population on the 7th day of the week = 5000 = 200*(r^6)
From this, you'll be able to find r. So, (1) is sufficient.

[rishijhawar]

Sandeep, thanks. However, I am wondering how to calculate the sixth root of r as r^6=25 assuming this is a problem solving sum (plz refer to my question again
Also, in my post too, I reached r^(n-1)=25 or r^6=25.
Not sure if this is in GMAT format, but the method would be helpful.
Experts, please help.
Thanks

[sandeeptalla450]

rishijhawar: It is important to understand that DS question checks the feasibility of finding an answer. Calculating the 6th root of 25 would be time consuming to say the least. I don't expect such a question in problem solving.

P.S.: You posted r^(n-1)=50. It should be 25.