**Quote:**

I didn't understand the explanation of the answer, because in statement (1) I can write *x* = 1/4 and the answer will still be an integer.

The basic question statement tells us that

*x* must be an integer. So

*x* = 1/4 is impossible.

The fact that

*x* is a positive integer is highly important in this question. Let us analyse statement (1): 9 × √(16

*x*) is an integer.

9 × √(16

*x*) = 9 × 4 ×√

*x* =

*a*, where

*a* is an integer

So √

*x* =

*a* / 36

*x* = (

*a* / 36)²

Remember, that

*x* is a positive integer, therefore

*a* must be divisible by 36 and therefore √

*x* =

*a* / 36 is an integer as well.