Question

If x / y is an integer, which of the following statements must be true?

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

Only E) is true. If I were to arbitrarily pick x = 2.2 and y =1.1, then I could show that A), B), C), and D) to be false, given x/y = 2.2/1.1 = 2 (which is an integer). However for E), if we define x/y = n where n is an integer, then by rearranging terms, we can show x = n*y where n still equals an integer and our original equation is still valid.