Solution for PS question #100 from OG 13

Question

Need a simpler solution for the following question from OG 13, as I could not understand the explanation.
Question- 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?

Options a)5 b)50 c)10^5 d)5^10 e)8^10 - 3^10

GMATGuruNY · Answer

syashveersingh wrote:Need a simpler solution for the following question from OG 13, as I could not understand the explanation.
Question- 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?

Options a)5 b)50 c)10^5 d)5^10 e)8^10 - 3^10

Another approach:

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

Brent@GMATPrepNow · Answer

syashveersingh wrote:Need a simpler solution for the following question from OG 13, as I could not understand the explanation.
Question- 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?

Options a)5 b)50 c)10^5 d)5^10 e)8^10 - 3^10

Every time we proceed from n to n+1 in the scale, the intensity is multiplied by a FACTOR OF 10.
To illustrate:
Let n=5.
Then n+1 = 6.
From a reading of 5 to a reading of 6, the intensity is multiplied by a factor of 10.

Let a reading of 3 = 1.
From a reading of 3 to a reading of 8 -- a total of FIVE positions in the scale -- the intensity will be multiplied by a factor 10 five times:
1 * 10� = 10�.

The correct answer is C.

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Solution for PS question #100 from OG 13

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