Formulas: On a scale that measures the intensity of a certai

II 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) 5
(B) 50
(C) 10^5
(D) 5^10
(E) 8^10 - 3^10

I had trouble understanding and breaking down the question !
Thanks.

uptowngirl92 wrote:My solution:
according to the stem:
READING.........................VALUE
n..................................x
n+1..............................10x
n+2..............................100x
n+3...............................1000x

so,let n=x=1.Therefore,following the above pattern:
1............................1
2.............................10
3..............................100
4...............................1000

Reading of 8=10^7
Reading of 3=10^2

QUERIE:How is 10^7 10^5 times greater than 10^2??should'nt the answer be 10^7-10^2.Seems to me that instead of substracting,we are dividing. why?this is not clear.

Stuart Kovinsky wrote:

II 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) 5
(B) 50
(C) 10^5
(D) 5^10
(E) 8^10 - 3^10

I had trouble understanding and breaking down the question !
Thanks.

The stem is basically telling us that each number on the scale is 10 times the intensity of the previous number.

For example, if a reading of 1 had a value of 10, then a reading of 2 would have a value of 10*10, a reading of 3 would have a value of 10*10*10 and so on.

So, if we want to compare a reading of 8 to a reading of 3, we've gone up by 5 "ranks" of intensity, which means we're multiplying by 10*10*10*10*10 = 10^5.

As an aside, this is how the Richter scale works for measuring earthquakes (which is why a reading of 7.0 is MUCH worse than a reading of 6.0) and, for the geeks in the crowd, how the Warp speed scale works on Star Trek!