Question

If x / y is an integer, which of the following statements need NOT always be true?

Select ALL such statements.

A. both x and y are integers
B. x is an integer
C. either x or y is negative
D. y / x is an integer
E. x = ny where n is an integer

Answer 1

A. \(\dfrac{0.4}{0.2} = 2\) therefore the values do not need to be integers.
B. Using the example from A, x does not need to be an integer.
C. One of the values could be negative resulting in a negative integer or both values could be negative resulting in a positive integer or both values could be positive resulting in a positive integer
D. Using the example from A, the reciprocal would equal \(\dfrac{1}{2}\)
E. plug in some values for n and see when it is true or false. Be sure to use negatives, 0, positives and decimals in your test values.