Walkabout wrote:
If n is a positive integer, is the value of b - a at least twice the value of 3^n - 2^n?
(1) a= 2^(n+1) and b= 3^(n+1)
(2) n = 3
The Question asks:
b - a > 2*(3^n - 2^n)The answer should be a definitive yes/no
Statement 1:a= 2^(n+1) and b= 3^(n+1)
Lets take the smallest possible value of a Positive Integer i.e 1 and put it in for "n"
3^(1+1) - 2^ (1+1) > 2*(3^1 - 2^1)
3^2 - 2^2 > 2* (3 - 2)
9 - 4 > 2 *1
5>2 (a definitive answer)
Lets test another number (just to be on the Safe Side), lets test n=2
3^(2+1) - 2^ (2+1) > 2*(3^2 - 2^2)
3^3 - 2^3 > 2* (9 - 4)
27 - 8 > 2* 5
19> 10 (a definitive answer)
Thus, Sufficient.Statement 2:
n=3
Let's Put it in the in-equality b - a > 2*(3^n - 2^n)
b - a> 2*(3^3 - 2^3)
b - a> 2*(27 - 8)
b - a> 2*(19)
b - a> 38
If, b=100 and a=10, than definitive answer
If, b= 2 and a= 10, than definitive answer
But since it doesn't provide any value for either "a" or "b"
Thus,
Not SufficientTherefore the answer is