On a scale that measures the intensity of a certain phenomenon…

Reading Time: 2 minutes

Last Updated on May 3, 2023

GMAT OFFICIAL GUIDE PS

Solution:

To solve this problem we need to 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. Let’s say n is 2. This means 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

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