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Problem Solving

by RiyaR » Wed Sep 24, 2014 7:54 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 [email protected] » Wed Sep 24, 2014 8:52 am
Hi RiyaR,

The logic behind this question is similar to how earthquakes are measured, but you don't need to recognize that to answer the question correctly. Like many questions on the Quant section, this question needs to be "played with" a bit.

We're told that with each "+1" increase in the "level of intensity" on a scale, the intensity of a phenomenon increases 10 times.

So, for example:
Level 1 = Z intensity
Level 2 = 10Z intensity
Level 3 = 100Z intensity
Level 4 = 1,000Z intensity
Etc.

We're asked how many TIMES greater "level 8" is than "level 3", so I can either continue on with the table or use "exponent math"

The table....
Level 3 = 100Z
Level 4 = 1,000Z
Level 5 = 10,00Z
Level 6 = 100,000Z
Level 7 = 1,000,000Z
Level 8 = 10,000,000Z

Level 8/Level 3 =
10,000,000Z/100Z =
10,000 times greater

Using "exponent math", we know that every level is "10x" greater than the previous level. Since Level 8 is "5 levels" above Level 3, that would be 10^5 greater.

Final Answer: C

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Rich
Contact Rich at [email protected]
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by Brent@GMATPrepNow » Wed Sep 24, 2014 9:47 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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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