Priyaranjan 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
Please excuse me for writing the answer choices C,D&E in this way.
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Solution:
Let's carefully examine the information in the first sentence. We are told that "a reading of n + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n."
Let's practice this idea with some real numbers to get a feel for what's happening. Let's say n is 2. It follows that n + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.
Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.
Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.
We have found a pattern, which can be applied to the problem presented in the stem:
3 is one unit away from 2, and thus a reading of 3 is
10^1 times as great as the intensity of a reading of 2.
4 is two units away from 2, and thus a reading of 4 is
10^2 times as great as the intensity of a reading of 2.
5 is three units away from 2, and thus a reading of 5 is
10^3 times as great as the intensity of a measure of 2.
We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is
10^5 times as great as the intensity corresponding to a reading of 3.
Answer:
C
