Problem Solving incorrect sentences?

[neotinx]

Hello everyone,

My first post here on BeattheGMAT website..

I was reading the question sentences from the 12th OG guide (#99)

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 correct
d. 5^10
e. (8^10)-(3^10)


I have interpreted this question in following ways:

The question remains confusing as it implies that the reading is simply 10 times a reading on n+1. By that logic, the equation is:
n+1 = 10n
A reading if 8 is 70 and a reading of 3 is 20. Difference is 50 (choice B), which is WRONG.

The equation should be written as:

n + 1 = 10^n

Per the equation: reading of 8 is 10^7 and reading of 3 is 10^2. The results differ by a factor of 10^5 or [10^7/10^2] = 10^5


This question is really unclear the way it is written. It clearly states 10 'TIMES' the intensity corresponding to the reading of n. This means it should be 10n not 10^n
The language of the question is very confusing...the correct answer is C


I know that the correct answer is C and I should have solved it as 10^n but I just can't grasp the concept. Is it me or the question is phrased incorrectly?

[eagleeye]

Hi Neotinx:

Welcome to the BTG community.

The language in this case is fine. You are interpreting it wrongly. The statement says
"The intensity corresponding to" n+1 is 10 times that of n. This means that intensity is related to reading n in some way. In the math world, we would depict such a relationship by
Intensity (I) = f(n) ; where f represents some sort of function.

Now let's look at this particular problem. Keeping in mind that I=f(n), and new intensity is f(n+1)
we are told that f(n+1)=10*f(n) (New Intensity is 10 times the previous intensity). We don't know what f(n) is exactly. But we can still solve questions.

Now expanding the pattern, for n=1,2,3 etc. we see that.
for n=0, f(0+1)=10*f(0) => f(1)=10*f(0)
for n=1, f(1+1)=10*f(1) => f(2)=10*f(1) = 10* (10*f(0)) = 10^2*f(0)
for n=2, f(3)=10*f(2) = 10^3*f(0) etc.
So we can see the pattern.
Then we need to find f(8)/f(3)
It will be (10^8*f(0))/(10^3*f(0)) = 10^5.

Your mistake was assuming that the reading is 10 times the previous reading. The relationship is not between the "reading" but the corresponding "intensities".

To interpret it the way you wanted it to be, it should have said, "the new reading of n+1 equals 10 times the previous reading of n. I am sure (100%), the more you practice such questions, you will get a penchant for setting up the equations correctly. If it's a hard one, there are experts here to help. Good luck.

Let me know if this helps

[neotinx]

Thank you so much!

Sometimes it's hard to grasp the concept/instruction of a question such as this one!

You just blew my mind with a crystal-clear explanation! Again, thanks a lot