In the solution, it shows that the two quantities can be cross-multiplied so in this case 216 went to the denominator of Quantity B and 2^x came to the denominator of Quantity A. My question is, is this operation something that we could generalize for all other QC questions (ofc except for the cases where denominator would become 0 or we might get a not defined answer) because in the prepswift strategy videos, this specific operation wasn’t covered so I was a little confused. It would be great if you could confirm this.
Yes, you can. The idea is similar to solving an inequality. Whatever preserves the inequality would also then preserve the relationship between two quantities. Alternatively, whatever operation doesn’t preserve the inequality would thus not preserve the relationship between the quantity.
For example, if you multiply both sides by some negative quantity and then surmise that QA > QB, then remember to flip the final answer to actually have QB > QA.
Thanks again! 