hard · GMAT Quant
A positive integer n is processed in three stages. Stage 1 replaces n by the greatest integer less than or equal to 3n/4. Stage 2 replaces the result x by the least integer greater than or equal to 2x/3. Stage 3 replaces the result y by the greatest integer less than or equal to 5y/6. The final result is 30. In a counterfactual process, each greatest-integer rounding is changed to least-integer rounding and the least-integer rounding is changed to greatest-integer rounding.
What is the sum of all possible original values n for which the counterfactual final result is also 30?
- 74
- 145
- 219
- 216
- 290
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