Let's say the Reading at 3 = 1
Reading at 4 = 1 *10
Reading at 5 = 1*10*10
Reading at 6 = 1*10*10*10
Reading at 7 = 1*10*10*10*10
Reading at 8 = 1*10*10*10*10*10 = 1 *10^5

Answer 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

A reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n.
Put another way:
Every time we move up one position in the scale, the intensity is multiplied by a FACTOR OF 10.
Thus:
A reading of 2 is 10 times a reading of 1.
A reading of 3 is 10 times a reading of 2.
A reading of 4 is 10 times a reading of 3.

A reading of 8 is how many times...a reading of 3?
Let a reading of 3 = 1.
Since every subsequent reading increases by a factor of 10, we get:
Reading of 4 = 10*1 = 10.
Reading of 5 = 10*10 = 100.
Reading of 6 = 10*100 = 1000.
Reading of 7 = 10*1000 = 10,000.
Reading of 8 = 10*10,000 = 100,000.

Since a reading of 8 = 100,000 and a reading of 3 = 1, a reading of 8 is 100,000 times a reading of 3.

The correct answer is C.

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

Answer is C