\(p\) is the smallest perfect cube greater than \(1\) such that the difference between the tens digit of \(p^2\) and the

[Vincen]

\(p\) is the smallest perfect cube greater than \(1\) such that the difference between the tens digit of \(p^2\) and the units digit of \(p^2\) is \(2.\) If \(Z=1\cdot 2\cdot 3\cdot\cdots \cdot p,\) then the total number of factors of \(Z\) is

A. 5
B. 8
C. 14
D. 96
E. 192

Answer: D

Source: e-GMAT