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operations on rational numbers

This topic has 4 expert replies and 0 member replies
marat_isr Newbie | Next Rank: 10 Posts Default Avatar
Joined
06 Mar 2014
Posted:
3 messages

operations on rational numbers

Post Fri Mar 03, 2017 8:37 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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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    Post Fri Mar 03, 2017 8:45 am
    Quote:
    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

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    Thanked by: marat_isr
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    Post 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.

    GMAT assassins aren't born, they're made,
    Rich

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    Post 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 = 10^5.

    The correct answer: C

    Hope this helps!

    Relevant book: Manhattan Review GMAT Word Problems Guide

    -Jay
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