mathT

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The integer 90can be expressed as the sum of z consecutive integers. The value of z could be any of the following except

A) 3
B) 4
C) 5
D) 6
E) 9

  • maths -

    If the first integer is n+1, the consecutive integers are: n+2, ...n+z.

    If 90 is the sum of these z consecutive integers then...

    90 = sum{i=1 to z} n+i
    90 = zn + sum{i=1 to z} i
    90 = zn + z(z+1)/2

    .: n = (180-z(z+1))/2z

    Testing the given values of z:
    A) z=3 => n = (180-3*4)/6
    B) z=4 => n = (180-4*5)/8
    C) z=5 => n = (180-5*6)/10
    D) z=6 => n = (180-6*7)/12
    E) z=9 => n = (180-9*10)/18

    One of these 'n' is not an integer.
    One of these 'n' does not belong.
    Can you tell me which one?

  • mathT -

    (D)6

    6x + 5*6/2 = 90
    6x + 15 = 90
    6x = 75
    x is not an integer

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