Answer:
The answer is C.
Step-by-step explanation:
The key to solve the problem is the equation given
y = 2z which means that<u> y is always an even number.</u>
For example:
let z = 1; y = 2(1) y = 2;
let z = 2; y = 2(2) y = 4;
let z = 3; y = 2(3) y = 6;
And we know that for any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms.
For example:
Set of numbers: [1,2,3,4,5,6] ;
Sum of the set: 1+2+3+4+5+6 = 21 ;
Number of terms of the set: 6;
Therefore, 21 is not a multiple of 6.
But for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
For example:
Set of numbers: [1,2,3,4,5,] ;
Sum of the set: 1+2+3+4+5 = 15 ;
Number of terms of the set: 5;
Therefore, 15 is a multiple of 5.
And that's why we know that if y is always an even number (y = 2z), the sum of the consecutive integers (x) is not a multiple of y, therefore x/y cannot be an integer.
