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

I had trouble understanding and breaking down the question ! Any thoughts ... approaches to solve this one.
Thanks.

N=N
N+1=10*N

So:
3=3
3+1 = 4= 10*3
5= 10* 4 = 10*10*3
...
8=10^5 * 3

Diff i.e 8 - 3 = 10^5 (ans = C)

Sorry HefAR I dont follow your explanation ...

Consider it this way:
A reading of n+1 is 10 times a reading of n.

So a reading of 4 is 10 times a reading of 3.
A reading of 5 is 10 times a reading of 4, which is 10 times a reading of 3, so a reading of 5 is 10^2 times a reading of 3.
Similarly, a reading of 6 is 10 times a reading of 5, so a reading of 6 is 10^3 times a reading of 3.

In essence, every increase in the reading by 1 results in an increase in the magnitude by a factor of 10. Since 8 is 5 units more than 3, a reading of 8 must be 10^5 times the magnitude of a reading of 3.

Incidentally, this is called a logarithmic scale and it's how the Richter scale works. So a 4.0 earthquake is 10 times more intense than a 3.0 earthquake.

Rey
(in earthquakey San Francisco)

That makes sense. Thanks.

We're glad to help!

I too did not get the problem until I read the explanation provided by rfernandez. However in the book, the explanation still uses 10^8 and 10^3. Since the intensity reading was 8 then n should be 7, correct? And a reading of 3, n would be 2, such that n + 1 = 3.

So the correct explanation to the answer should be:

(10^7) / (10^2) = which would give the same answer of 10^5.

The official guide has it as (10^8) / (10^3)

Please correct me if I'm wrong.

Not quite. The n and n+1 are used simply to define the relationship between any reading (n) and the next reading up (n+1).

Given the nature of the problem, though, you end up with the same answer because what matters is how far apart the exponents are from each other, not their actual values.