2. Percentages and Percent Change

Percent means 'per hundred.' The foundational relationship is:

part = percent x whole (where percent is written as a decimal)

This one formula handles three types of SAT® percent questions:

• Find the part: 'What is 30% of 80?' --> 0.30 x 80 = 24.
• Find the percent: '24 is what percent of 80?' --> 24/80 = 0.30 = 30%.
• Find the whole: '24 is 30% of what number?' --> 24/0.30 = 80.

Percent increase and percent decrease are the two most commonly tested percent applications on the SAT®:

percent change = (new value - original value) / original value x 100

• A salary rises from $50,000 to $57,500: change = 7,500 / 50,000 = 0.15 = 15% increase.
• A price drops from $200 to $170: change = -30 / 200 = -0.15 = 15% decrease.

Shortcut multipliers speed up calculations:

• Increase by 20%: multiply by 1.20.
• Decrease by 15%: multiply by 0.85.
• Apply a 40% markup then a 40% discount: multiply by 1.40 x 0.60 = 0.84 (an 16% net decrease -- NOT back to the original!).

Worked example: A store buys a jacket for $80 and marks it up 25%. A week later they put it on a 20% off sale. What is the final sale price?

• After markup: $80 x 1.25 = $100.
• After discount: $100 x 0.80 = $80.
• The final price is $80 -- back to cost, but NOT the original retail.

• Successive percent changes are multiplicative, not additive. A 25% increase followed by a 25% decrease gives 1.25 x 0.75 = 0.9375, a net loss of 6.25%.
• Percent of a percent: '20% of 15%' means 0.20 x 0.15 = 0.03 = 3%.

⚠️ Common mistake: dividing by the NEW value instead of the ORIGINAL when calculating percent change. Percent change always uses the starting value as the denominator.

💡 Tip: convert percent to a decimal multiplier and multiply -- it is faster and more reliable than the formula, especially on the calculator-active section.