## OG - PS - #99

Math questions and topics from the Official Guide and Quantitative Review books. Please try to follow the posting pattern (e.g. OG - DS - #142) to allow for easier searches. Questions posted in the GMAT Math section regarding the OG have been moved here.
mww7786

### OG - PS - #99

#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 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 3?

a. 5
b. 50
c. 10^5 correct
d. 5^10
e. (8^10)-(3^10)
GMAT 5/18

mww7786,

I think the best way to solve this would be to use real (smart) numbers. Let's make n = 1. Therefore,

When n = 1, intensity = 1
When n = 2 (n+1), intensity = 10
When n = 3, intensity = 100 (Same as 10^2)
etc, etc
When n = 8, intensity = 10,000,000 (Same as 10^7)

Therefore, the intensity when n = 8 is 10^5 times greater than the intensity when n = 3.

Hope this helps!
ManhattanGMAT Staff

Posts: 108
Joined: Mon Aug 07, 2006 10:33 am
Location: Chicago, IL

That looks great, GMAT 5/18 . A slight modification: you can start with n=3:

n=3, intensity=x

then n=4, intensity = (10)x

then n=5, intensity = 10(10)x = (10^2) x

then n=6, intensity = 10(10)(10)x = (10^3) x

then n=7, intensity = 10(10)(10)(10)x = (10^4) x

then n=8, intensity = 10(10)(10)(10)(10)x = (10^5) x

As soon as you notice the pattern - that the exponent of the 10 goes up 1 for each step along the way to n=8, you can just count the number of steps to n=8 and realize that the exponent has to be 10^5 times higher at n=8 than at n=3.