If the equation y² - 2my + n = 0 has 12 as one of its roots, where n is less than 130 and is divisible by 8 and the equation z² - 2mz + r = 0 has 7 as one of its roots, and m(≠ 7) is a prime number, then what is the value of 2m + r - n?

12 is a root of y^2 - 2my + n = 0, so 144 - 24m + n = 0 => n = 24m - 144. n < 130 and divisible by 8. If m=7, n=24(7)-144=24 (divisible by 8). But m != 7. If m=8, n=48. If m=9, n=72. If m=10, n=96. If m=11, n=120. If m=12, n=144 (too big). 7 is a root of z^2 - 2mz + r = 0, so 49 - 14m + r = 0 => r = 14m - 49. Test m=11: n=120, r=14(11)-49=105. 2m+r-n = 22 + 105 - 120 = 7.