Posted by **fran** on Sunday, September 15, 2013 at 1:06am.

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 -
**Graham**, Sunday, September 15, 2013 at 6:29am
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 -
**Steve**, Sunday, September 15, 2013 at 6:33am
(D)6

6x + 5*6/2 = 90

6x + 15 = 90

6x = 75

x is not an integer

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