Is x an integer?

From statement 1 alone
5x is an integer
For x=1/5, 5x is an integer (x is not an integer)
For x=1, 5x is an integer (x is an integer)
Hence we can't answer the question from Statement 1 with a definite 'yes' or 'no'

From statement 2 alone
for x= 1, \(\frac{5}{x}\) is an integer (x is an integer)
for x=1/5, \(\frac{5}{x}\) is an integer (x is not an integer)
Hence we can't answer the question from Statement 2 with a definite 'yes' or 'no'

Combining both statements
If x=1, then 5x is an integer and 5/x is also an integer (x is an integer)
if x=1/5, then 5x is an integer and 5/x is also an integer (x is not an integer)

Even by combining both the statements, we cannot answer the question with a definite 'yes' or 'no'

Answer E