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Thread: Are You Scientifically Literate?1430 days old

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    Quote Originally Posted by Rugevit View Post
    Similar types questions and also question related to sequences and series basically puzzles are often asked in the tests for certain type of job applications in large corporations. HR send you to a testing centre as part of the application. Some professionals find these tests disrespectful.
    I had one of those for my current job. Number sequences are pretty easy, though. Although the bulk of my test was Raven's Progressive Matrices, which are also easy.

    https://en.m.wikipedia.org/wiki/Rave...ssive_Matrices
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    Here is puzzle like inequality exercise from school program for all interested to try

    Prove that х^12 - x^9 + x^6 - x^3 + 1 > 0 for all real x > 0

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    Quote Originally Posted by Rugevit View Post
    Here is puzzle like inequality exercise from school program for all interested to try

    Prove that х^12 - x^9 + x^6 - x^3 + 1 > 0 for all real x > 0
    0 multiplied by or to the power of anything is always 0, then there's the +1. So it's 1
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    Quote Originally Posted by DragonRouge View Post
    0 multiplied by or to the power of anything is always 0, then there's the +1. So it's 1
    x > 0 means all real numbers (infinite numbers) greater than zero that can be substituted for x . These numbers could be 0.0025, 0.1, 3, 10, 2384 etc
    Last edited by Rugevit; 2015-07-26 at 20:27.

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    The inequality can be written as x^12 + x^6 + 1 > x^9 + x^3 for x > 0 for x is real.


    For 1 > x > 0:

    x^12 < x^9 < 1 and x^6 < x^3 < 1 which means x^12 + x^6 < x^9 + x^3 < 1
    which also means that adding 1 to either of both sides makes its value always higher than the other so

    x^12 + x^6 + 1 > x^9 + x^3

    For x >= 1:

    x^12 > x^9 and x^6 > x^3 so x^12 + x^6 > x^9 + x^3 so evidently

    x^12 + x^6 + 1 > x^9 + x^3

    Q.E.D.

    Luckily it's still at mid-high school level.
    Last edited by Danielion; 2015-07-26 at 21:02.
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    Quote Originally Posted by Rugevit View Post
    Similar types questions and also question related to sequences and series basically puzzles are often asked in the tests for certain type of job applications in large corporations. HR send you to a testing centre as part of the application. Some professionals find these tests disrespectful.
    I misread your math question. But yeah to get back to this... these tests actually are not to measure IQ or anything, they're to see if you're capable of working under pressure. They have impossible time limits and built to observe if you get too stressed and give up, or keep on trucking. It's impossible to get them all correct in the time limit, so it's best to just do the easy ones and take a guess at the hard ones.

    These tests are trolling you, pretty much. So yeah, I guess it's disrespectful.

    - - - Updated - - -

    Quote Originally Posted by asingh View Post
    I took the first 5 questions. Got them all wrong. Stopped.

    Physics Bachelors. Guess all that 15 years of programming has ruined it. LOL.

    @DragonRouge: Your score was impressive.
    You work in IT, you never learned how to "cheat" on multiple choice tests that are required for certifications? Well, not really cheating, just tips on how to eliminate wrong answers from the choices when you don't know the answer.

    Multiple choice usually works like this.

    1. Two that make absolutely no sense
    2. One to trick you
    3. The correct answer

    This is one I didn't know and got correct using this method:

    45. In quantum mechanics, the physical constant used to describe the sizes of quanta – denoted as h – is named after what German physicist?

    1. Albert Einstein and Erwin Schrodinger just make no sense - not them, also Schrodinger was Austrian, not German
    2. Werner Heisenberg is the one to trick you, his surname starts with H - not him
    3. The correct answer is Max Planck.
    Last edited by DragonRouge; 2015-07-26 at 22:03.
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    Quote Originally Posted by Danielion View Post
    The inequality can be written as x^12 + x^6 + 1 > x^9 + x^3 for x > 0 for x is real.


    For 1 > x > 0:

    x^12 < x^9 < 1 and x^6 < x^3 < 1 which means x^12 + x^6 < x^9 + x^3 < 1
    which also means that adding 1 to either of both sides makes its value always higher than the other so

    x^12 + x^6 + 1 > x^9 + x^3

    For x >= 1:

    x^12 > x^9 and x^6 > x^3 so x^12 + x^6 > x^9 + x^3 so evidently

    x^12 + x^6 + 1 > x^9 + x^3

    Q.E.D.

    Luckily it's still at mid-high school level.


    Well done!

    There are many solutions to the problem. One possible solution is to use the summing of geometric series. Geometric series are still being taught in schools?

    So, х^12 - x^9 + x^6 - x^3 + 1 is sum of a geometric series with the coefficient -x^3. Therefore, х^12 - x^9 + x^6 - x^3 + 1 = (x^15+1)/(x^3+1) > 0 for all real x >0

    Alternatively, one may do some curly algebra re-writing х^12 - x^9 + x^6 - x^3 + 1 as (x^6-x^3 +1)^2 + (x^3)(x^3-1)^2 > 0 for all real x > 0

    ---

    Let's make the problem a bit more difficult proving that х^12 - x^9 + x^6 - x^3 + 1 >0 for all real x.

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    Quote Originally Posted by Rugevit View Post
    Geometric series are still being taught in schools?
    Not sure. Series are at least. I don't have a flawless school record myself.
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    I think I would have got an ever higher score if the test had been in swedish, since there were a couple of unusual words I didn't understand.

    But I do know the english names for most chemical element.

    Fun fact: I think Brimstone is a cooler name than Sulfur (in swedish Svavel). Brimstone is the Biblical name for Sulfur, as I allready knew and what was asked in the test.
    The Future was better before

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    Quote Originally Posted by Danielion View Post
    Not sure. Series are at least.
    In that case instead of using formula for sum of a geometric series we can solve the problem using the alternating series, which is essentially the same solution.




    I don't have a flawless school record myself.

    I never had flawless school records either.

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