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

## Answer this Question

## Related Questions

- math - A. Four times one odd integer is 14 less than three times the next even ...
- math - there are 8 consecutive integers that add up to 31. Only two of the ...
- algebra1 - two consecutive integers such that the sum of 3 times the frist ...
- math, algebra - 2a+2ab+2b I need a lot of help in this one. it says find two ...
- math - 1. The largest of five consecutive integers is twice the smallest. Find ...
- algebra1 - Find to consecutive integers that the sum of 3 times the first ...
- quad. eq. - find 3 consecutive integers such that the product of the second and ...
- Math ( Number Theory ) - How many numbers from 1 to 1000 inclusive can be ...
- math - i dont get this question consecutive integers are integers that differ by...
- Algebra - A.Write and solve an equation to find three consecutive integers with ...

More Related Questions