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Intensity scale readings

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Intensity scale readings

by BlueDragon2010 » Sat Feb 08, 2014 9:09 am
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
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by Brent@GMATPrepNow » Sat Feb 08, 2014 9:11 am
BlueDragon2010 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
If we start with a NICE NUMBER, it won't take us long to list the intensity for each reading, starting at a reading of 3 and stopping at a reading of 8.

Say a reading of 3 means an intensity of 1
So, a reading of 4 means an intensity of 10
A reading of 5 means an intensity of 100
A reading of 6 means an intensity of 1,000
A reading of 7 means an intensity of 10,000
A reading of 8 has an intensity of 100,000

100,000 is 100,000 times bigger than 1.
Since 100,000 = 10^5, the correct answer is C

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Brent
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by Patrick_GMATFix » Sat Feb 08, 2014 9:36 am
Each reading (n+1) is 10 times higher in intensity than the one below (n), so the next higher reading (n+2) will be 100 times (10^2) higher than the initial reading (n). Each time the reading is increased by 1, the intensity is multiplied by 10. So going from a reading of 3 to a reading of 8 will multiply the intensity by 10 5 times (multiply by 10^5). The full solution below is taken from the GMATFix App.

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