HKDSE Math Problem

圖片參考：https://s.yimg.com/rk/HA00430218/o/1132875718.png


From the range condition, we know that
(40 + k) - (10 + h) ≥ 33
That is, k - h ≥ 3 ...(1)

From the stem and leaf setting, we need to be careful that
0 ≤ h ≤ 4 ...(2)
0 ≤ k ≤ 9 ...(3)

From (1), k ≥ h + 3
From (2), 3 ≤ h + 3 ≤ 7

Therefore, k ≥ 3.
With (3), we have 3 ≤ k ≤ 9.

Thus, Statement II must be true.

For Statement I, a counter example is:
{ h = 4 > 3
{ k = 9
Then, the range is 35 ≥ 33.

For Statement III, a counter example is:
{ h = 0
{ k = 9
Then, k - h = 0 > 5, and the range is 39 ≥ 33.