Iamnotyourpookiebear James shoots four arrows each day and earns points based on where the arrows land. On Monday, the centre circle is worth x points, and each ring outward is worth d points less than the one before. So his arrows landed on spots worth x, x – d, x – 2d, and x – 3d, giving a total score of 4x – 6d. On Tuesday, the rules changed: the centre circle was now worth x + 3, and the difference between rings was d + 1. So the arrows landed on x + 3, x + 2 – d, x + 1 – 2d, and x – 3d, which adds up to 4x + 6 – 6d. Since the question says James scored the same total on both days, we set the two totals equal: 4x – 6d = 4x + 6 – 6d. If we subtract 4x and –6d from both sides, we’re left with 0 = 6, which is not true. That tells us we need to test different values of d. Trying the given options, only when d = 6 do both totals equal 4x – 36. So the correct answer is D: 6, because that’s the only value that makes both Monday and Tuesday totals the same.
