OG 12 #98

[jimmynicho]

On a scale that measures the intensity of a certain phenomen, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of three?
a)5
b)50
c)10^5
d)5^10
e)8^10-3^10

[vasbli]

first lets get the question right:

On a scale that measures the intensity of a certain phenomen, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n.

8 is how many times as great as the intensity corresponding to a reading of three?

Again, GP question, with n+1=10n. hence, n=10(n-1), and by combining
n+1=10x10(n-1)=10^2(n-1)

the 8th term of the GP is 10^5 the 3rd term

[ssmiles08]

You can also do this by the counting method since the numbers 3 and 8 arent that far apart.

let 3 have an intensity of i.

3 = i
4 = 10*i
5 = 100*i
6 = 1000*i
7 = 10^4*i
8 = 10^5*i

therefore the intensity of 8 is 10^5 times greater than 3

(C)