Question:
If $p$ and $q$ are co-prime numbers, then $p^{2}$ and $q^{2}$ are
(a) coprime
(b) not coprime
(c) even
(d) odd
Solution:
We know that the co-prime numbers have no factor in common, or, their HCF is 1.
Thus, $p^{2}$ and $q^{2}$ have the same factors with twice of the exponents of $p$ and $q$ respectively, which again will not have any common factor.
Thus we can conclude that $p^{2}$ and $q^{2}$ are co-prime numbers.
Hence, the correct choice is (a).