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Formulas: On a scale that measures the intensity of a certai

by II » Sun Apr 13, 2008 4:42 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 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
(D) 5^10
(E) 8^10 - 3^10

I had trouble understanding and breaking down the question !
Thanks.
Last edited by II on Mon May 05, 2008 1:39 am, edited 1 time in total.
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Re: Formulas and functions ...

by Stuart@KaplanGMAT » Sun Apr 13, 2008 8:24 pm
II 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 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
(D) 5^10
(E) 8^10 - 3^10

I had trouble understanding and breaking down the question !
Thanks.
The stem is basically telling us that each number on the scale is 10 times the intensity of the previous number.

For example, if a reading of 1 had a value of 10, then a reading of 2 would have a value of 10*10, a reading of 3 would have a value of 10*10*10 and so on.

So, if we want to compare a reading of 8 to a reading of 3, we've gone up by 5 "ranks" of intensity, which means we're multiplying by 10*10*10*10*10 = 10^5.

As an aside, this is how the Richter scale works for measuring earthquakes (which is why a reading of 7.0 is MUCH worse than a reading of 6.0) and, for the geeks in the crowd, how the Warp speed scale works on Star Trek!
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by richardwang6430 » Tue Apr 15, 2008 6:06 pm
I will go with C
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by uptowngirl92 » Tue May 05, 2009 12:18 am
My solution:
according to the stem:
READING.........................VALUE
n..................................x
n+1..............................10x
n+2..............................100x
n+3...............................1000x

so,let n=x=1.Therefore,following the above pattern:
1............................1
2.............................10
3..............................100
4...............................1000

Reading of 8=10^7
Reading of 3=10^2

QUERIE:How is 10^7 10^5 times greater than 10^2??should'nt the answer be 10^7-10^2.Seems to me that instead of substracting,we are dividing. why?this is not clear.
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by sacx » Tue May 05, 2009 3:01 am
uptowngirl92 wrote:My solution:
according to the stem:
READING.........................VALUE
n..................................x
n+1..............................10x
n+2..............................100x
n+3...............................1000x

so,let n=x=1.Therefore,following the above pattern:
1............................1
2.............................10
3..............................100
4...............................1000

Reading of 8=10^7
Reading of 3=10^2

QUERIE:How is 10^7 10^5 times greater than 10^2??should'nt the answer be 10^7-10^2.Seems to me that instead of substracting,we are dividing. why?this is not clear.
the question asks 'how many times' not 'by how much'. When it says 'times' you are looking for multiples.

eg. by how many times is 100 greater than 10. the answer to this would be 10. You can rephrase this question as, 100 = 10*x, what is the value of x?

BUT when you say by how much then you need to subtract.

by how much is 100 greater than 10. the answer is 90.
SACX
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by rahatali » Thu Oct 31, 2013 5:23 pm
Stuart Kovinsky wrote:
II 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 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
(D) 5^10
(E) 8^10 - 3^10

I had trouble understanding and breaking down the question !
Thanks.
The stem is basically telling us that each number on the scale is 10 times the intensity of the previous number.

For example, if a reading of 1 had a value of 10, then a reading of 2 would have a value of 10*10, a reading of 3 would have a value of 10*10*10 and so on.

So, if we want to compare a reading of 8 to a reading of 3, we've gone up by 5 "ranks" of intensity, which means we're multiplying by 10*10*10*10*10 = 10^5.

As an aside, this is how the Richter scale works for measuring earthquakes (which is why a reading of 7.0 is MUCH worse than a reading of 6.0) and, for the geeks in the crowd, how the Warp speed scale works on Star Trek!
If a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n, then how would I know that a reading of n+2 corresponds to an intensity that is 10×10 times, it can be 20 times. To me, this question does not provide sufficient information. Please help.
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by [email protected] » Thu Oct 31, 2013 6:49 pm
Hi rahatali,

The key to this question is understanding the different between "N" and "N+1"

We're told that these two values are "intensities" and that "N+1" is "10 times more intense" than "N"; this essentially means that IF you add 1 to any "intensity", then the intensity gets 10 times bigger.

So, let's say N = 3 has an intensity of 1....

N = 3 ---> intensity of 1
N = 4 ---> intensity of 10 (10 times the intensity of N = 3)
N = 5 ---> intensity of 100 (10 times the intensity of N = 4)
N = 6 ---> intensity of 1,000 (10 times the intensity of N = 5)
N = 7 ---> intensity of 10,000 (10 times the intensity of N = 6)
etc.

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Contact Rich at [email protected]
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