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#### OG - PS - #99

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 Post subject: OG - PS - #99  Posted: Sat Jun 02, 2007 8:43 pm
 #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)

 Post subject:   Posted: Sun Jun 03, 2007 1:38 pm
 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!

 Post subject:   Posted: Wed Jun 06, 2007 11:49 am
 ManhattanGMAT Staff

Posts: 108
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. -Jad

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