A binary search tree is used to locate the number 43. Which of the following…

Why A is Correct:

Path Check: Starting at 61, we search for 43. Since 43 < 61, we move left. From 52, we again move left, so the upper bound becomes 52. The subsequent numbers 14, 17, and 40 tighten the lower bound sequentially (14 < 17 < 40 < 43). Since 43 lies between 40 and 52, the sequence follows BST ordering rules.

   61       [Target 43 < 61: Go Left]  -> Window: (under 61)
     /
    52       [Target 43 < 52: Go Left]  -> Window: (under 52)
   /
  14         [Target 43 > 14: Go Right] -> Window: (between 14 and 52)
   \
    17       [Target 43 > 17: Go Right] -> Window: (between 17 and 52)
     \
      40     [Target 43 > 40: Go Right] -> Window: (between 40 and 52)
       \
       [43]  Found! (43 is safely between 40 and 52)

Why C is Correct:

Path Check: The sequence establishes a lower bound at 10 and an upper bound at 65. Every subsequent jump narrows the search window down logically: 31 (new lower bound), 48 (new upper bound), and 37 (final lower bound). Since 37 < 43 < 48, the target value fits perfectly inside the valid range.

   10         [Target 43 > 10: Go Right] -> Window: (above 10)
   \
    65       [Target 43 < 65: Go Left]  -> Window: (between 10 and 65)
   /
  31         [Target 43 > 31: Go Right] -> Window: (between 31 and 65)
   \
    48       [Target 43 < 48: Go Left]  -> Window: (between 31 and 48)
   /
  37         [Target 43 > 37: Go Right] -> Window: (between 37 and 48)
   \
   [43]      Found! (43 is safely between 37 and 48)

Why D is Correct:

Path Check: The sequence starts at the high end, continuously establishing and lowering the upper boundary constraints: 81 -> 61 -> 52. From 52, the path jumps left to 14, establishing a lower bound. The path then moves right to 41. Since the final target constraint sits legally within the established active range (41 < 43 < 52), this is a completely possible path.

        81   [Target 43 < 81: Go Left]  -> Window: (under 81)
       /
      61     [Target 43 < 61: Go Left]  -> Window: (under 61)
     /
    52       [Target 43 < 52: Go Left]  -> Window: (under 52)
   /
  14         [Target 43 > 14: Go Right] -> Window: (between 14 and 52)
   \
    41       [Target 43 > 41: Go Right] -> Window: (between 41 and 52)
     \
     [43]    Found! (43 is safely between 41 and 52)