Let \( \rho = Corr[X, Z] \). Then we have the following correlation matrix for \( X, Y, Z \):

\( \begin{bmatrix} 1 & 0.6 & \rho \\ 0.6 & 1 & 0.7 \\ \rho & 0.7 & 1 \end{bmatrix}\)

I think the question want you to check whether this matrix is positive-definite or not.

One easy way to check is the Sylvester's Criterion:

http://en.wikipedia.org/wiki/Sylvester_criterion
which essentially require you to have a positive determinant. When you compute it, you should obtain a quadratic polynomial in \( \rho \) and thus you should obtain a bound for it.