MGMAT CAT Exam PS | Another Way of doing it

Hi, there. I'm happy to help with this.

Prompt:
The number of antelope in a certain herd increases every year at a constant rate. If there are 500 antelope in the herd today, how many years will it take for the number of antelope to double?

When we talk about populations growing at a rate, it always means a multiplier. The population is being multiplied by the same multiplier from one year to the next --- for example, it's multiplied by 1.2 each year (that would be a 20% growth rate).

Let's say that multiplier is r. The population now is 500, and we want to know, how many years (n) will it take to double?

1000 = 500*r^n
2 = r^n

Basically, if we knew the value of r, or had a way of finding the value of r, the multiplier, then we could find n.

Statement #1
Ten years from now, there will be more than ten times the current number of antelope in the herd.

This is an inequality, which is not going to help us solve an equation.

It's saying, essentially, 10 < (r^10) ---- so r could be just more than the tenth root of ten*, or r could be 1.5 or 2 or 3 or 14 or anything larger. If the multiplier is r = 2, then the population doubles in one year. If the multiplier is the square-root of two, then the population doubles in two years. Different values give different answers, which is not surprising since an inequality, by its very nature gives a whole infinity of possible values. This statements, by itself, is insufficient.

*the tenth root of ten --- the tenth root of anything is a really small root, and small roots are relatively close to 1. That's all you are expected to know about the tenth root of ten without a calculator. With a calculator, we can find: 10^(0.1) = 1.258925412

Statement #2
If the herd were to grow in number at twice its current rate, there would be 980 antelope in the group in two years.

Let R be the new multiplier.
This is telling us that 900 = 500*(R^2).
That's an equation, that would allow us to solve for R. (Admittedly, we can't actually find the decimal value of R without a calculator, but that's not the point on DS --- from pure logic, one has enough mathematical information to be able to solve for R.)
Once we find the value of R, we can easy find r --- for example, say R = 1.6 (it doesn't, but just for simplicity) --- that's a 60% growth rate, and half of that is a 30% growth rate, which means r = 1.3. So, if we know R, we can find r. If we know r, we can answer the prompt question. Therefore, this statement, by itself, is sufficient.

Answer = B

You may find these blogposts helpful:
a) https://magoosh.com/gmat/2012/understand ... -the-gmat/
b) https://magoosh.com/gmat/2012/percent-ch ... -the-gmat/

Does all this make sense? Let me know if you have any further questions.

Mike