hard · GMAT Quant
An automated logistics center processes shipments using two pricing regimes. For a package of weight w kilograms, where w is an integer, the base processing fee is 2w^2 + 5 dollars. However, if the total shipping volume V = w(w - 3)(w + 4) exceeds 120 cubic meters, a high-volume surcharge of 3w + 15 dollars is triggered and added to the base fee.
For how many positive integer package weights w ≤ 8 does the total processing fee (including any applicable surcharge) equal an odd integer strictly less than 100 dollars?
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