Step-by-Step Solution
A cube ends in 3 only when the number itself ends in 7, because 73=343. So the units digit is 7. Answering 3 copies the cube's last digit — a rule that works for 0, 1, 4, 5, 6 and 9 but fails for the swapping pairs 2/8 and 3/7. (The number is 67, and 673=300763.)
Answer: D) 7
Key idea: Estimating cube roots
For non-perfect cubes, bracket the cube root between two consecutive integers.
Example: ∛100. We know 43=64 and 53=125. So 4 < ∛100 < 5. Closer to 5 (100 is closer to 125 than 64). Refined estimate: ∛100 ≈ 4.64.
For perfect cubes, look at the last digit (last digit rule for cubes: each digit cubes to a unique last digit). 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0.