x² - 11x + |p| = 0 has integer roots. How many integer values can 'p' take?

2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.

Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.

a1x + b1y + c1z = d1, a2x + b2y + c2z = d2, a3x + b3y + c3z = d3.

Which of the following statements if true would imply that the above system of equations does not have a unique solution?
i. a1/a2 = b1/b2 = c/1c2 ≠ d1/d2
ii. a1/a2 = a2/a3 ; b1/b2 = b2/b3
iii. a1, a2, a3 are integers; b1, b2, b3 are rational numbers, c1, c2, c3 are irrational numbers

Equation x² + 5x – 7 = 0 has roots a and b. Equation 2x² + px + q = 0 has roots a + 1 and b + 1. Find p + q.