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KCC's Quizzes AQQ272 about a division giving its double

This week, we will relax a little bit with a quite easy problem AQQ273:

Good luck and try to be among the first ones!

Please share your answer to view other submitted answers
  • 1/2.

    Indeed:  a/a  = 2a,  implies  a is not 0 (we can't divide by 0), leaving:  a  = 2a^2,  or 1=2a.

  • This quizz has a lot of initial challenges.
    The visual cues above the question itself hints to a division of dice which leads to a double six: statistics here?
    Then the question itself is laced with brackets, and a minus sign, so maybe I need to do some subtraction as well ;-).
    But removing the expressions in the brackets, the question is: which number divided by itself equals 2x itself, maybe there is more than 1 answer.
    So the math is:
    - for which x:
    \frac{x}{x}=2x =>
    1=2x =>
    x=\frac{1}{2}

    I was inclined to also nominate -1/2, but the sign turns out wrong.

  • Under modular arithmetic  (residue modulo) there is a unique solution to  1 = 2x  (mod  y)   -- Gauss' notation
     that is:                                                                                                            x = (y+1)/2 

    So, since there is an infinite number of odd numbers, there is an infinite number of solutions, one for each (mod  y), y being a odd integer.

    y=3,  x = (3+1)/2  = 2.  Indeed 2x = 4 =  1 (mod 3)   since 4 residue modulo 3  get a rest of 1.
    y=5,  x = (5+1)/2  = 3. Indeed  2x = 6  = 1 (mod 5), 

    etc. They all satisfy                  2x = 1  (mod y)

  • x/x = 2x ==> x = 0.5

    Zero would work if 0 divided by 0 were defined as 0  Relaxed

  • 1/2 or 0.5 is the only number which then results in 1 (double of 0.5), when divided by itself.

  • You can write this as x/x = 2x and multiplying both sides by x arrive at x = 2x^2

    Rearranging, we get 2x^2 – x = 0 then factoring we get x(2x-1) = 0

    For the equation to be zero, either factor must be zero

    So, either x = 0 or 2x-1=0 => x=0.5, so the number is either 0 or 0.5

    Anything divided by zero is undefined, so strictly-speaking the only solution is 0.5.

  • Bingo  , you get it, congratulations (too easy for you...)!

  • Wow, I learn something... I was not aware about the modular arithmetic method...

  • Bravo  ! You found the right answer!