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OG 12 #98

by dreamv » Sat Feb 18, 2012 1:17 pm
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 intesity 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
Last edited by dreamv on Mon Feb 20, 2012 6:15 pm, edited 1 time in total.
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by pemdas » Sat Feb 18, 2012 2:47 pm
Denote intensity of reading as W and write functions n=W,(n+1)=10W or 10*n
Then n=3, (3+1)=10W or 10*3; ((3+1)+1)=10*10*3 and ((3+1)+1)+1))=10*10*10*3. Continue till 3+5=8. Thus, 3*10^5 and the required will be (3*10^5) : 3 = 10^5

answer [spoiler]10^5[/spoiler]
dreamv 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 intesity 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. 10^3
D. 5^10
E. 8^10 - 3^10
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by dreamv » Mon Feb 20, 2012 6:42 pm
Thanks for explanation. You are correct. OA is C. 10^5. There was a typo in my original post on C.
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by Anurag@Gurome » Mon Feb 20, 2012 7:54 pm
dreamv 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 intesity 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
Reading of n+1 corresponds to an intensity that is 10 times the intesity corresponding to a reading of n means every number on the scale is 10 times the previous number.
So, we can say that f(n + 1) = 10 * f(n)
Let us assume that the intensity corresponding to a reading of 3 be X, then f(3) = X
So, f(4) = 10 * f(3) = 10X
f(5) = 10 * f(4) = 10² * f(3)
f(6) = 10^3 * f(3) and so on
Hence, f(8) = 10^5 * f(3)

The correct answer is C.
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