25 thoughts on “Modulus Examples -1

  1. Dear J,

    Is the no: of integer points = 37? i.e X varies from -3 to 3 right? And the is the figure in the form of a triangle seated on top of a rectangle?


  2. Dear J,

    So plotting them will give a triangle of base -3 to +3 and height 0 to 3 and a rectangle of sides -3 to 3 and 0 to -3. By this iam getting area as 42 i.e 7 * 4 + 0.5 * 7 * 4. What am i doing wrong here?


  3. for x = -2, we can also get y= -4, as:
    -2 -y -(2+y) = 4,
    which gives -2y = 8,
    y= -4
    because when value from modulus is considered, it will be negative? this way for one value, many values of y can come.. whats wrong in it?

  4. ohh.. ok, actually i intentionally took it because i thought negatives will be taken as it is, like we do in modulus , if |x| <= 5, then we take -5<x<5, like that.. anyways,, thanks

  5. sir, i am having hard time for getting the range for values here…like for x=2, i am getting 2y=0 so y=0 correct…then what should be the next step to get y=-2…if i open the mod as -2-y-y-2=4 then i am getting y=-4…what step i am doing wrong here…?

    • Hi Sir,

      Thanks again for the wonderful post.
      I have one query with regards to finding the range for x and y.
      I have understood that the basic concept you are using for the same is making sure mod of x or y should not be equal to a negative number, that’s where you stop.
      Having said that for the equation lxl+lyl+lx+yl=4 when I sub x=3 I get the values of y=-1,-2.
      Now just looking at the values of y I am not able to say if it as acceptable value or not.
      I did substitute back to the main equation and find out that it was not satisfying the equation hence I could discard this value.
      Is this the way you are following too?
      Could you please help me on this.

      • Not exactly. In lxl+lyl+lx+yl=4 when I put x=3 I get l3l+lyl+l3+yl=4 which is |y| + |y+3| = 1 which gives no values (the sum of the distances of y from 0 and 3 should add up to 1, which is not even possible!). But yeah, it is always safer to check your answer by plugging back in, if time permits.


  6. sir like for x=2 first i am doing putting |x| as x and getting y=0 as result then putting |x| as -x …for this i am getting y=-4 but the range is from -2 to 0 …i know i am making a very silly mistake but please can you point me to it…

    • The RHS is a number here as well? So I have no idea what you want to ask I’m afraid. (If you mean what if it is 20 instead of 4, same logic, once you know how it works for 4 you should easily be able to extrapolate to 20)


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