Problem Solving

shivshankar054 wrote:On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?

A reading of 4 = 10 times of a reading of 3
A reading of 5 = 10 times of a reading of 4 = 10^2 times of a reading of 3
A reading of 6 = 10 times of a reading of 5 = 10^3 times of a reading of 3

So, a reading of 8 = 10^(8 - 3) times of a reading of 3 = 10^5 times of a reading of 3

The correct answer is C.

Another approach to solve this problem is interpreting the reading as some function f(n)

So, we can say that f(n + 1) = 10*f(n)

So, f(4) = 10*f(3)
f(5) = 10*f(4) = (10^2)*f(3)
f(6) = (10^3)*f(3) and so on

Hence, f(8) = (10^5)*f(3)

The correct answer is C.

On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?

A. 5
B. 50
C. 10^5
D. 5^10
E. 8^10 - 3^10

Another approach is to start with a nice number.
Say a reading of 3 means an intensity of 1
So, a reading of 4 means an intensity of 10
A reading of 5 means an intensity of 100
A reading of 6 means an intensity of 1,000
A reading of 7 means an intensity of 10,000
A reading of 8 has an intensity of 100,000

100,000 is 100,000 times bigger than 1.
Since 100,000 = 10^5, the correct answer is C

Cheers,
Brent