Percentages Pattern - Foundations

Basic percentage operations: finding the part, percent, or whole

Percentage questions are among the most common on the SAT. The foundation pattern tests whether you can use the basic percentage formula in all three directions.

The Core Formula (Three Forms)

Every percentage problem boils down to three quantities: the part, the percent, and the whole.

$\text{Part} = \dfrac{\text{Percent}}{100} \times \text{Whole}$

Depending on what the question asks for, you rearrange:

• Find the percent: $\text{Percent} = \dfrac{\text{Part}}{\text{Whole}} \times 100$
• Find the part: $\text{Part} = \dfrac{\text{Percent}}{100} \times \text{Whole}$
• Find the whole: $\text{Whole} = \dfrac{\text{Part} \times 100}{\text{Percent}}$

Find the Percent (Most Common)

A university received a total of $40{,}000$ applications for admission. Of those, $9{,}600$ applicants were accepted. What percentage of applicants were accepted?

A) 14%
B) 24%
C) 34%
D) 76%

The part is $9{,}600$ and the whole is $40{,}000$.
$\text{Percent} = \dfrac{9{,}600}{40{,}000} \times 100 = 0.24 \times 100 = 24\%$
Answer: B

Gotcha — The Complement Trap: Choice D (76%) is $100\% - 24\%$, the percentage who were not accepted. If you see the complement as an answer choice, double-check which group the question actually asks about.

Find the Whole

$15$ is $30\%$ of what number?

A) 4.5
B) 30
C) 50
D) 450

Set up the equation: $0.30 \times x = 15$
$x = \dfrac{15}{0.30} = 50$
Answer: C

Gotcha — Multiplying Instead of Dividing: Choice D (450) comes from $15 \times 30$. When the question says "X is P% of what," you divide: $\dfrac{X}{P/100}$. Choice A (4.5) comes from computing 30% of 15 — that's the wrong direction.

Find the Part

A basketball team attempted 80 shots and made 24 of them. What percentage of their shots did the team make?

A) 24%
B) 33%
C) 56%
D) 30%

$\text{Percent} = \dfrac{24}{80} \times 100 = 0.30 \times 100 = 30\%$
Answer: D

Gotcha — Raw Number as Percent: Choice A (24%) uses the count of made shots as the percent. Always divide first, then multiply by 100.

What to Do on Test Day

• Identify the three quantities (part, percent, whole) and figure out which one is missing.
• "What percent" → divide the part by the whole, then multiply by 100.
• "X% of what number" → divide the part by the decimal form of the percent.
• Watch for the complement. If the question asks "what percent were accepted," don't accidentally compute the percent rejected.
• Key formula: $\text{Percent} = \dfrac{\text{Part}}{\text{Whole}} \times 100$