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Help with Arithmetic Problem

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21 May 2010, 08:16
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Hi guys, Can some one explain step by step this problem, because i didn't understand the book explanation.

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 with exponent 5
D) 5 with exponent 10
E) 8 with exponent 10 - 3 exponent 10

I hardly understand what they are asking for.

Thanks
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Re: Help with Arithmetic Problem [#permalink]

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21 May 2010, 08:30
Hi guys, Can some one explain step by step this problem, because i didn't understand the book explanation.

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 with exponent 5
D) 5 with exponent 10
E) 8 with exponent 10 - 3 exponent 10

I hardly understand what they are asking for.

Thanks

Basically we are given that each number on the scale is 10 times the previous number. For example:
If reading of n=3 is 5 then the reading of n=4 would be 5*10 --> the reading of n=5 would be 5*10^2 --> the reading of n=6 would be 3*10^3. Therefore the reading of 8 will be 10^5 times as great as the reading of 3 (the power of 10 goes up by 1 for each step in reading and as there are 5 steps from 3 to 8 then the reading of 8 will be 10^5 times as great as the reading of 3).

Or think about it this way: we have functional relationship: when we increase the reading by 1 the intensity increases 10 times the previous one: $$f(n+1)=10*f(n)$$.

So if $$f(3)=x$$, then $$f(4)=10*f(3)=10x$$ and so on. Therefore $$f(8)=10^5*f(3)$$.

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Re: Help with Arithmetic Problem [#permalink]

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21 May 2010, 12:25
Hi guys, Can some one explain step by step this problem, because i didn't understand the book explanation.

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 with exponent 5
D) 5 with exponent 10
E) 8 with exponent 10 - 3 exponent 10

I hardly understand what they are asking for.

Thanks

Scale - Corresponding intensity
intensity of (n +1) - 10(intensity of n)
intensity of 8 - x(intensity of 3)

We need to find out x ?

8 - 10(intensity of 7)
so we go down to 3 we are just multiplying each time by 10. So in this case the power of 10 will be 8-3 = 5

x = 10^5 <--- C
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Re: Help with Arithmetic Problem [#permalink]

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21 May 2010, 19:04
Thanks for your help. Very good explanations.
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Re: Help with Arithmetic Problem [#permalink]

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18 Nov 2011, 12:26
n = 1
n+1 = 10

similarly:
3 = k
4 = 10k
8 = 10^5k

so it is C.
Re: Help with Arithmetic Problem   [#permalink] 18 Nov 2011, 12:26
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