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operations on rational numbers

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by marat_isr » Fri Mar 03, 2017 8:37 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 DavidG@VeritasPrep » Fri Mar 03, 2017 8:44 am
marat_isr 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
Let's call the intensity at a reading of 3: x.
Reading of 4: 10x
Reading of 5: (10^2) * x
Reading of 6: (10^3) * x
Reading of 7: (10^4) * x
Reading of 8: (10^5) * x

Thus a reading of 8, or 10^5 * x, would be 10^5 times a reading of 3, or x. The answer is C
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by Brent@GMATPrepNow » Fri Mar 03, 2017 8:45 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
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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by [email protected] » Fri Mar 03, 2017 9:55 am
Hi marat_isr,

GMAT questions are often written in such a way that you can approach the question in a number of different ways and still get the correct answer. The level of 'complexity' with which you choose to approach each prompt is up to you, but you'd be surprised how often there's a 'simple' way to deal with a prompt.

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.

Thinking in those terms, it's not difficult to get to the correct answer.

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by Jay@ManhattanReview » Sat Mar 04, 2017 1:32 am
marat_isr 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
Hi marat_isr,

The meaning of the phrase, "a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n" is simply that the next reading is 10 times the previous reading. And this is true for all the readings on the given scale.

Say the reading for 1 = 1;
Thus, the reading for 2 = 1*10 = 10;
Similarly, the reading for 3 = 10*10 = 10^2
Similarly, the reading for 4 = 10*10 = 10^4
.
.
.
Similarly, the reading for 8 = 10*10 = 10^7

=> Reading for 8 / Reading for 3 = 10^7 / 10^2 = [spoiler]10^5[/spoiler].

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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by Jeff@TargetTestPrep » Thu Apr 19, 2018 5:04 pm
marat_isr 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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