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20 Tricky Problems · Key Topics

Don't fall for
the trap.

These problems are designed to trick you. Read every word carefully. Common SAT word problem traps are highlighted in each question.

Algebra & Linear Equations

Q 01 Linear Equations Easy
🔑
Memory Point · "TOTAL = SUM" Identify what variable you need. The question asks for one value — but must you find another first?

A store sells notebooks for $3 each and pens for $1.50 each. Maria buys a total of 10 items and spends exactly $21.

⚠️ Trap: You need to set up two equations. Don't just divide $21 ÷ 10.

How many notebooks did Maria buy?

Answer:
Q 02 Percent Change Medium
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Memory Point · "NOT SYMMETRIC" A 20% increase followed by a 20% decrease does NOT return to the original. Percent change is always relative to the CURRENT base.

A jacket originally costs $80. Its price is increased by 25%, then decreased by 20%.

⚠️ Trap: 25% − 20% = 5% increase is WRONG. Calculate step by step.

What is the final price of the jacket?

Answer: $
Q 03 Rates & Work Medium
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Memory Point · "ADD RATES, NOT TIMES" Combined work: 1/A + 1/B = 1/T. Add the RATES (jobs per hour), not the hours.

Machine A can complete a job in 6 hours. Machine B can complete the same job in 4 hours. If both machines work together, how many hours will it take to complete the job?

⚠️ Trap: Do NOT average the times: (6+4)/2 = 5 is WRONG.

Express your answer as a fraction or decimal.

Answer:
Q 04 Slope & Linear Models Medium
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Memory Point · "SLOPE = RATE OF CHANGE" In a word problem, slope = "change per unit." The y-intercept = starting value when x = 0.

A taxi charges a flat fee of $3.50 plus $2.25 per mile. A ride-share charges a flat fee of $1.00 plus $2.75 per mile.

After how many miles will both services cost the same amount?

⚠️ Trap: Set equations equal to each other — don't calculate each side separately with a guessed mileage.
Answer:
Q 05 Age Problems Hard
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Memory Point · "TIME SHIFTS EVERYONE" If n years pass, ADD n to EVERY person's age. Write out both "now" and "future" ages.

Today, Emma is 3 times as old as her daughter Lily. In 10 years, Emma will be twice as old as Lily.

⚠️ Trap: In 10 years, BOTH ages increase by 10, not just one.

How old is Emma today?

Answer:

Ratios, Proportions & Mixtures

Q 06 Mixture Problems Hard
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Memory Point · "AMOUNT × CONCENTRATION" Mixture equation: Amount₁ × % + Amount₂ × % = Total Amount × Target %.

A chemist has a 20% acid solution and a 50% acid solution. How many liters of the 20% solution must be mixed with 6 liters of the 50% solution to produce a 30% acid solution?

⚠️ Trap: Don't average 20% and 50% to get 35%. Use the mixture equation.
Answer:
Q 07 Proportional Reasoning Medium
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Memory Point · "UNIT CONVERSION CHAIN" Multiply by fractions that cancel units. Set up: (given unit) × (want/have) × ... = answer.

A car travels at a constant speed of 60 miles per hour. How many feet does the car travel in 5 seconds?

1 mile = 5,280 feet  |  1 hour = 3,600 seconds
⚠️ Trap: Don't multiply 60 × 5 directly. You must convert units.
Answer:
Q 08 Average / Mean Hard
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Memory Point · "SUM = MEAN × COUNT" Work backwards: find the missing SUM, not the missing average directly.

The average score of 5 students on a test is 78. When a 6th student joins, the average drops to 75. What score did the 6th student receive?

⚠️ Trap: Don't subtract 78 − 75 = 3 and call it the answer. Calculate total sums.
Answer:

Quadratics & Functions

Q 09 Quadratic Word Problems Hard
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Memory Point · "MAX HEIGHT = VERTEX" For h(t) = −at² + bt + c, vertex time = −b/(2a). Plug back in to find max height.

A ball is thrown upward. Its height in feet after t seconds is modeled by:

h(t) = −16t² + 64t + 5

What is the maximum height the ball reaches, in feet?

⚠️ Trap: The maximum is NOT at t = 0 and NOT when the ball hits the ground.
Answer:
Q 10 Consecutive Integers Medium
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Memory Point · "CONSECUTIVE = n, n+1, n+2" Consecutive EVEN/ODD integers: n, n+2, n+4. Not n, n+1, n+2.

The product of two consecutive positive odd integers is 195. What is the larger integer?

⚠️ Trap: Odd integers differ by 2, not 1. Use n and n+2, not n and n+1.
Answer:
Q 11 Function Notation Hard
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Memory Point · "f(a+b) ≠ f(a) + f(b)" Always substitute the whole expression into the function first, THEN simplify.

Let f(x) = 2x² − 3x + 1.

What is the value of f(x + 1) − f(x) when x = 3?

⚠️ Trap: f(x+1) − f(x) ≠ f(1). You must compute f(4) and f(3) separately.
Answer:

Geometry & Measurement

Q 12 Area & Perimeter Medium
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Memory Point · "SCALE FACTOR ≠ AREA FACTOR" If dimensions scale by k, AREA scales by k². If scale = 3×, area = 9×.

A rectangle has a length of 12 cm and a width of 5 cm. A second rectangle is similar to the first, and its length is 18 cm.

What is the area of the second rectangle, in cm²?

⚠️ Trap: Scale factor = 18/12 = 1.5. Area scales by 1.5² = 2.25, not 1.5.
Answer:
Q 13 Circles Hard
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Memory Point · "ARC = (θ/360) × CIRCUMFERENCE" Sector area = (θ/360) × πr². Arc length = (θ/360) × 2πr.

A circle has a radius of 6. A central angle of 120° creates a sector.

What is the area of this sector? (Leave answer in terms of π.)

⚠️ Trap: The sector fraction is 120/360 = 1/3 — don't use 120 directly.
Answer:
Q 14 Similar Triangles Medium
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Memory Point · "MATCH CORRESPONDING SIDES" Set up ratios with sides in the same position. Cross-multiply to solve.

A 6-foot person stands next to a tree. The person's shadow is 4 feet long, and the tree's shadow is 22 feet long. Both shadows are cast at the same time.

How tall is the tree, in feet?

⚠️ Trap: Set up person height/shadow = tree height/shadow — don't add or subtract shadows.
Answer:

Statistics & Data Analysis

Q 15 Median & Outliers Hard
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Memory Point · "OUTLIERS CHANGE MEAN, NOT MEDIAN" An outlier heavily shifts the mean. The median (middle value) is resistant to outliers.

Seven employees have salaries (in thousands): 32, 35, 38, 41, 45, 48, 210.

Which is greater — the mean or the median — and by approximately how much?

⚠️ Trap: The value 210 is an outlier. The mean is pulled up significantly; the median is not.

Enter the mean salary (in thousands, rounded to nearest whole number).

Mean ≈
Q 16 Two-Way Tables Medium
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Memory Point · "CONDITIONAL PROBABILITY = PART / ROW TOTAL" "Given that…" = conditional. Denominator is the relevant row or column total, NOT the grand total.

A survey of 200 students asked about their grade level and whether they have a part-time job:

Has JobNo JobTotal
Junior3565100
Senior6040100
Total95105200

What is the probability that a randomly selected student who has a job is a Senior? Express as a percentage.

⚠️ Trap: Denominator is 95 (total with jobs), NOT 200 (all students).
Answer: ~

Inequalities & Absolute Value

Q 17 Inequalities Hard
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Memory Point · "FLIP WHEN DIVIDE BY NEGATIVE" When multiplying or dividing an inequality by a negative number, FLIP the inequality sign.

A school needs at least 300 points to qualify for a competition. A team scores p points per round. They have already played 8 rounds and scored an average of 32 points per round. They have 4 rounds remaining.

What is the minimum average score per round they must achieve in the remaining rounds to qualify?

⚠️ Trap: Don't subtract — set up an inequality, then solve for p.
Answer:
Q 18 Exponential Growth Hard
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Memory Point · "A × r^t vs A × (1+r)^t" Exponential growth: P(t) = P₀(1+r)^t. The rate r must be in decimal form.

A bacteria culture starts with 500 cells and doubles every 3 hours. How many cells will there be after 12 hours?

⚠️ Trap: After 12 hours, number of doublings = 12/3 = 4, NOT 12.
Answer:
Q 19 Distance, Rate, Time Hard
🔑
Memory Point · "AVERAGE SPEED ≠ AVERAGE OF SPEEDS" Average speed = Total Distance ÷ Total Time. Never average the two speeds directly.

Alex drives from City A to City B at 60 mph, then immediately returns at 40 mph. The distance between the cities is 120 miles.

What is Alex's average speed for the entire round trip?

⚠️ Trap: Average speed is NOT (60 + 40)/2 = 50 mph. Use total distance ÷ total time.
Answer:
Q 20 Systems & Word Problems Hard
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Memory Point · "DEFINE VARIABLES EXPLICITLY" Write what each variable means. "Let x = …" before solving. This prevents mixing up what you solved for.

A movie theater sells adult tickets for $12 and child tickets for $7. On Saturday, the theater sold 150 tickets and collected $1,450.

⚠️ Trap: The question asks for the number of CHILD tickets — don't accidentally report adult tickets.

How many child tickets were sold?

Answer:
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