gettinit wrote:
if x^2+5y=49, is Y an integer?
1) 1<x<4
2) x^2 is an integer
I have an issue with the
kaplan answer here. My answer would be c because stmt one tells you x is between integers 1 and 4, but it could be a non-integer so not sufficient, and 2 is not sufficient because x could be an integer. However, together the stmts satisfy as x could only be 2 or 3 and 2^2 and 3^2 both agree with the equation making y an integer. Please advise.
Hi!
You've misinterpreted statement (2).
From (2), we know that x^2 is an integer. Based on this, you've erroneously concluded that x must be an integer as well.
However, that's not the case. If x = root2 or root3, x^2 will still be an integer. Moreover, root2 and root3 both satisfy statement 1 as well. In fact, all we know is that:
root1 < x < root16,
so x could be root2, root3, root4, root5, ...., root 15. root4 and root9 are both integers, but none of the others are.
So, even combined, we can't determine whether y is an integer.