Scale that measures

[sal2]

This is an OG question.

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?

The way the question is phrased, I see 2 ways to set it up, each producing a very different answer.

How would you do it?
Sal

[papgust]

This question is already discussed. Please check this,
https://www.beatthegmat.com/og-intensity ... 49553.html

[sal2]

I understand that's the way they want you to set it up, but the language of the question was unclear to me. I wasn't sure if it should set up as follows:
n is the base value on the scale, so solve n+1=n*10, which gives you a value of 10/9=n. Then do 1/9 + 8 = 73/9 and 1/9 + 3 = 28/9. Final answer 73/28
All it says is that n+1 is 10 times n on a scale. Please explain.

[papgust]

Ok. Let me try to make it clear. Be ready to visualize!

"..a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n."

You may have seen a normal traditional scale with both centimeter and millimeter readings. Assume the scale (in problem) as centimeter-millimeter scale. 10 millimeters = 1 centimeter.

Consider a centimeter as n here and millimeter as intensity level. According to the question, it says that 2 centimeters (i.e. n+1) is 10 times 1 centimeter (i.e. n). You can visualize the term (10 times) as millimeter reading. Ideally on a millimeter scale, 2 centimeters is 10 times 1 centimeter.

--- Here, you would raise a question that 2 centimeters is actually NOT 10 times 1 centimeter on a millimeter reading. But for the sake of understanding this question better, just visualize this concept and do not dive deep into the centimeter-millimeter concept. I really can't think of any better real-time example. This just came from top of my head.----

In a similar way, 3 centimeters is 10*10 times 1 centimeter on a millimeter scale.... and so on.

We are now asked to find "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?"

On a centimeter-millimeter scale, they have asked us to find "8 centimeters is how many times as great as 3 centimeters on a millimeter scale"

So, 8 centimeters is 10*10*10*10*10 times 3 centimeters on a millimeter scale. which is nothing but 10^5 times. Here is your answer.

Hope you understood the method now!