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On a scale that measures the intensity of a certain phenomen

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New post Updated on: 07 Dec 2012, 06:35
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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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Originally posted by mydreammba on 14 Jan 2012, 03:06.
Last edited by Bunuel on 07 Dec 2012, 06:35, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Problem solving  [#permalink]

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New post 13 Mar 2013, 10:24
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abusaleh wrote:
Can anyone give me proper explanation of this 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?
A) 5
B) 50
C) 10^5
D) 5^10
E) 8^10 - 3^10

Dear abusaleh,
This is a tricky question. It is based on logarithmic scales --- both the Richter scale for earthquakes and the decibel scale for the volume of sound follow this pattern.

It tell us if we we go from n to n+1 on the scale, the intensity is 10 times greater.

Start at 3. If we go from 3 to 4 on the scale, the intensity increases 10 times. Then from 4 to 5, it increases 10 times. Same, from 5 to 6, from 6 to 7, and from 7 to 8. There are five "steps" from 3 to 8, and each one of these steps increases the intensity by a factor of 10. That means, when we go from 3 to 8 on the scale, we multiply the intensity by 10 five times ---- 10*10*10*10*10 = 10^5

Answer = C

Does this make sense?

Mike :-)
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Re: maths problem  [#permalink]

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New post 07 Jun 2012, 01:52
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As the intensity increases 10 times every time

from 3 to 8, it increases 5 times. So,answer is 10^5
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On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 14 Jan 2012, 04:54
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kotela wrote:
Hey Guys i didn't understand the solution to the problem in OG 12 PS#98, can anyone please explain me the solution???


kotela it's better to post the question itself to get prompt replies. I guess you are talking about the following 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?
A. 5
B. 50
C. 10^5
D. 5^10
E. 8^10 - 3^10

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 5*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 \(f(8)=10^5*f(3)\).

Answer: C.

Hope it's clear.
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Re: OG12 PS#98  [#permalink]

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New post 14 Jan 2012, 07:28
Bunuel wrote:
kotela wrote:
Hey Guys i didn't understand the solution to the problem in OG 12 PS#98, can anyone please explain me the solution???


kotela it's better to post the question itself to get prompt replies. I guess you are talking about the following 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?
A. 5
B. 50
C. 10^5
D. 5^10
E. 8^10 - 3^10

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 \(f(8)=10^5*f(3)\).

Answer: C.

Hope it's clear.


Thanks a lot.....I will
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Re: maths problem  [#permalink]

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New post 07 Jun 2012, 02:09
gnan wrote:
As the intensity increases 10 times every time

from 3 to 8, it increases 5 times. So,answer is 10^5



thanks a lot that was very helpful
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Re: Problem solving  [#permalink]

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New post 13 Mar 2013, 13:13
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We know that:
\(f(n+1)=10f(n)\)

so \(f(8)=10f(7)\) , \(f(7)=10f(6)\) and so on...

\(f(8)=10*10*10*10*10f(3)\)

Each 10 represents a "step back"
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 19 Jul 2014, 02:47
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A soln. easy to understand-

For n=3, consider the intensity to be x.

For n+1 = 4 , we have [intensity*10 ]= 10x
For n+2 = 5 , we have [10x*10 ]= 100x
For n+3 = 6 , we have [100x*10 ]= 1000x
For n+4 = 7 , we have [1000x*10 ]= 10000x
For n+5 = 8 , we have [10000x*10 ]= 100000x

Now , for n = 8 -->100000x = 10^5 x
which is 10^5 times x, the original intensity at n=3
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 14 Aug 2015, 03:23
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mydreammba 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

n = 10^(n-1)*k , where n=1,2,3,.......
8 = 10^7*k
3 = 10^2*k
It implies 8 is 10^5 times of 3
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 28 Feb 2016, 11:27
mydreammba 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


According to Manhattan-Gmat, the GMAT is a test of foreign language.
Any reading is 10 times the previous reading, if the reading is increasing by 1.
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 02 May 2016, 07:18
mydreammba 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


To solve this problem we need to examine the information in the first sentence. We are told that “a reading of n + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n.”

Let’s practice this idea with some real numbers. Let’s say n is 2. This means that n + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.

Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.

Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.

We have found a pattern, which can be applied to the problem presented in the stem:

3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.

4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.

5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.

We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.

Answer C.
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 20 Mar 2017, 07:17
From question

n+1 = N * 10

say the readings are 1,10,100,1000,10^4,10^5 so on... Implies it is 5 times greater
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 21 Mar 2017, 04:12
mydreammba 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



we can say that f(n) = 10^n
f(8)/ f(3) = 10^8/10^3 = 10^5
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 03 Apr 2017, 00:05
The intensity of 3 is n.
8-3= 5

Therefore the intensity of 8 will be 5 times the intensity of 3.
Therefore the answer is 10^5.
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 25 Aug 2017, 00:16
what level question is this?
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New post 02 Dec 2017, 05:42
Honestly this question is very confusing for me.
Based on the question stem I cannot recognize that the intensity increases 10 times every time... :-(
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 05 Mar 2018, 13:03
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Hi All,

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.

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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 24 Sep 2018, 00:25
mikemcgarry wrote:
abusaleh wrote:
Can anyone give me proper explanation of this 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?
A) 5
B) 50
C) 10^5
D) 5^10
E) 8^10 - 3^10

Dear abusaleh,
This is a tricky question. It is based on logarithmic scales --- both the Richter scale for earthquakes and the decibel scale for the volume of sound follow this pattern.

It tell us if we we go from n to n+1 on the scale, the intensity is 10 times greater.

Start at 3. If we go from 3 to 4 on the scale, the intensity increases 10 times. Then from 4 to 5, it increases 10 times. Same, from 5 to 6, from 6 to 7, and from 7 to 8. There are five "steps" from 3 to 8, and each one of these steps increases the intensity by a factor of 10. That means, when we go from 3 to 8 on the scale, we multiply the intensity by 10 five times ---- 10*10*10*10*10 = 10^5

Answer = C

Does this make sense?

Mike :-)
Yeah , but whats the logic behind multiplying , why not add ?
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Re: On a scale that measures the intensity of a certain phenomen  [#permalink]

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New post 24 Sep 2018, 11:33
Hi Arpitkumar,

A few posts in this thread explain how the 'math' works (including the one directly above your post) - we're told that each increase of "+1" in a 'reading' translates to a "10 TIMES" increase in intensity. Since the question asks for how many 'TIMES GREATER' one INTENSITY is than another, then we are clearly going to be using multiplication. If the question had asked for the difference one READING over another, then we would use addition.

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Re: On a scale that measures the intensity of a certain phenomen &nbs [#permalink] 24 Sep 2018, 11:33
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