Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p × q = 2430, then what is the difference between p and q?

• Let the two-digit number p be represented as 10a + b, where a is the tens digit and b is the units digit.

• The reversed number q is then 10b + a.

• The product p × q is given as 2430, so (10a + b)(10b + a) = 2430.

• Expanding the equation gives 100ab + 10a² + 10b² + ab = 2430, which simplifies to 101ab + 10(a² + b²) = 2430.

• Testing integer values for a and b (digits 1-9), the pair a=3 and b=6 satisfies the equation: (36)(63) = 2268 (incorrect, re-evaluating).

• Correct factorization of 2430: 2430 = 2 × 3^5 × 5. The two-digit factors are 30 and 81 (no, digits not same), 45 and 54 (digits 4,5 and 5,4). Let's check 45 × 54. 45 × 54 = 2430.

• Thus, p = 45 and q = 54 (or vice versa). The difference |p - q| = |45 - 54| = 9.