Problem Solving

zachlebo 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

If we start with a NICE NUMBER, it won't take us long to list the intensity for each reading, starting at a reading of 3 and stopping at a reading of 8.

Say a reading of 3 means an intensity of 1
So, a reading of 4 means an intensity of 10
A reading of 5 means an intensity of 100
A reading of 6 means an intensity of 1,000
A reading of 7 means an intensity of 10,000
A reading of 8 has an intensity of 100,000

100,000 is 100,000 times bigger than 1.
Since 100,000 = 10^5, the correct answer is C

Cheers,
Brent

zachlebo 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 do not know how to set up this problem and am confused by the exponents.

c

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