A number is doubled, then 5 is subtracted from the result, and finally the difference is divided by 3 to get 7. What is the original number?

Work backward through the steps. The final result 7 came from dividing by 3, so before that the value was $7 \times 3 = 21$. Before subtracting 5, it was $21 + 5 = 26$. Before doubling, it was $26 \div 2 = 13$. The original number is 13, choice D. Check forward: $13 \times 2 = 26$, $26 - 5 = 21$, and $21 \div 3 = 7$. Choice A (11) fails the check: $11 \times 2 - 5 = 17$. Choice C (8) results from $\frac{21 - 5}{2}$, subtracting 5 instead of adding it when undoing the subtraction. Choice B (18) comes from skipping the undo of the doubling.