The SAT gives you the price after a discount, or the population after a year of growth, and asks what the number was before. Working forward and working backward feel similar, but they are opposite operations. Going forward you multiply by the percent factor. Going backward you divide by it.
Set it up as an equation and the direction takes care of itself. If a jacket costs 60 dollars after a 25 percent discount, then the sale price is 75 percent of the original, so 0.75 times the original equals 60. Dividing gives an original price of 80 dollars. Checking forward confirms it, since 25 percent of 80 is 20, and 80 minus 20 is 60.
The tempting wrong move is to take 25 percent of 60 and add it back, giving 75 dollars. That fails because the discount was a percent of the original price, not a percent of the sale price. Taking 25 percent of the smaller number removes less than was originally taken off. Whenever the percent refers to a number you do not have yet, that number has to be the variable.
Growth works the same way. If a town has 8,400 residents after a 5 percent increase, then 1.05 times the original equals 8,400, so the original is 8,400 divided by 1.05, which is 8,000. Notice that the answer is a round number, which is a common signal on the SAT that you divided in the right direction.
Tax and tip questions are the same structure wearing a different label. A restaurant bill of 64.80 dollars including 8 percent tax means 1.08 times the pre-tax amount equals 64.80, so the food cost 60 dollars. A question asking for the tax amount alone then wants 4.80, which is the difference, not the 64.80 or the 60.
Two changes in a row combine into one multiplier and you divide by that. If a price rose 10 percent and then fell 20 percent to reach 88 dollars, the combined multiplier is 1.1 times 0.8, which is 0.88, so the original was 88 divided by 0.88, or 100 dollars. Build the whole multiplier first, then do a single division.