SAT Math — Problem Solving and Data Analysis Guide

Chapter Overview & Weightage

Problem Solving and Data Analysis (PSDA) is the single largest slice of SAT Math — roughly 30% of your total score, spread across 15–17 questions. These questions don’t appear in the no-calculator section; they’re all in the calculator-allowed portion, which means speed and interpretation matter more than raw computation.

The good news: this is the most learnable category. Unlike Advanced Math (which needs deep algebraic intuition), PSDA rewards careful reading and pattern recognition. Most Indian students who prepare for board exams already have strong percentage and ratio foundations — we just need to retool that knowledge for SAT-style data questions.

Weightage Breakdown (2022–2025 SAT)

Year	Total PSDA Questions	Ratio/Rate/Proportion	Percentages/Units	Stats/Probability	Data Interpretation
2022	16	5	4	3	4
2023	15	4	4	4	3
2024	17	5	5	3	4
2025	16	5	4	3	4

The College Board confirmed PSDA stays at ~30% with the digital SAT (Bluebook). The distribution above holds for digital format as well.

Key Concepts You Must Know

Prioritised by how often each sub-topic appears on actual tests:

Tier 1 — Show up almost every test:

Setting up and solving proportions (unit rates, scaling)
Percent increase/decrease, percent of a percent
Reading two-way tables (conditional probability, marginal totals)
Interpreting linear and exponential models in context
Mean, median, and how outliers shift each

Tier 2 — Appear frequently, roughly 2–3 questions per test:

Unit conversion chains (miles per hour → feet per second, etc.)
Scatterplot line-of-best-fit: slope meaning, y-intercept meaning
Probability from tables (independent events, overlapping sets)
Margin of error and survey sampling concepts

Tier 3 — Appear occasionally, worth knowing:

Standard deviation (conceptual — you won’t calculate it, just compare)
Weighted averages and mixture problems
Evaluating claims from sample data (statistical inference)

Important Formulas

\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100

When to use: Any question asking “by what percent did X increase/decrease?” or “what is the percent error?” Always divide by the original value — the most common mistake is dividing by the new value.

\frac{a}{b} = \frac{c}{d} \implies ad = bc

When to use: Direct proportion questions, scaling recipes, map distances, unit rates. If two quantities vary proportionally, set up a ratio and cross-multiply. Works for rates too: Distance = Rate × Time.

P(\text{Event}) = \frac{\text{Number of favourable outcomes}}{\text{Total outcomes}}

For conditional probability from a two-way table:

P(A \mid B) = \frac{\text{Both A and B}}{\text{Total in B}}

When to use: The conditional form is what the SAT actually tests. They give you a table and ask “given that a student is in Grade 11, what is the probability they prefer X?” — restrict your denominator to Grade 11 total only.

\bar{x} = \frac{\sum x_i}{n}

Median rule (no formula, just logic): Adding a value above the median pulls the median up or keeps it same. Adding a value below pulls it down. Adding a value much larger than all others barely moves the median but pulls the mean up significantly.

When to use: Questions that add/remove/change one data point and ask which measure of center is affected.

y = a \cdot (1 + r)^t \quad \text{(growth)} \qquad y = a \cdot (1 - r)^t \quad \text{(decay)}

Where $a$ = initial value, $r$ = rate (as decimal), $t$ = time.

When to use: Any context involving population doubling, bacterial growth, compound interest, radioactive decay, or “increases/decreases by X% each year.”

Solved Previous Year Questions

PYQ 1 — Percent of a Percent (SAT March 2024)

Question: A store reduces the price of a jacket by 20%. During a weekend sale, the already-reduced price is further reduced by 15%. What is the overall percent decrease from the original price?

Solution:

Let the original price be $100 (using a smart number — always do this for abstract percent questions).

After the first reduction: $100 \times 0.80 = \$ 80$

After the second reduction: $80 \times 0.85 = \$ 68$

Overall decrease $= 100 - 68 = 32$

\text{Percent decrease} = \frac{32}{100} \times 100 = 32\%

Answer: 32%

The trap here: students add 20% + 15% = 35% and mark that. Wrong. The second reduction applies to the already reduced price, not the original. Successive percent changes never simply add — always chain the multipliers.

PYQ 2 — Two-Way Table and Conditional Probability (SAT October 2023)

Question:

	Prefers Morning	Prefers Evening	Total
Students	45	30	75
Teachers	15	10	25
Total	60	40	100

A person is selected at random from those who prefer the morning session. What is the probability that the selected person is a student?

Solution:

The question says “from those who prefer morning” — so our universe is only the Morning column total: 60 people.

Of these 60, students number 45.

P(\text{Student} \mid \text{Morning}) = \frac{45}{60} = \frac{3}{4}

Answer: 3/4 or 0.75

In conditional probability from tables, underline the “given that” clause and find its total first. That total becomes your denominator. This single habit eliminates most two-way table errors.

PYQ 3 — Scatterplot Interpretation (SAT Digital, 2024 Practice Test 1)

Question: A scatterplot shows the relationship between the number of hours studied per week ( $x$ ) and score on a standardised test ( $y$ ). The line of best fit has equation $y = 3.2x + 54$ .

(a) What does the slope represent in this context? (b) A student studied 10 hours per week. What score does the model predict?

Solution:

(a) The slope is 3.2. In a linear model $y = mx + b$ , the slope tells us: for every 1-unit increase in $x$ , $y$ increases by $m$ units.

Here: for each additional hour studied per week, the predicted score increases by 3.2 points.

(b) Substitute $x = 10$ :

y = 3.2(10) + 54 = 32 + 54 = 86

Predicted score: 86

SAT almost always asks for slope interpretation in words, not just the numerical answer. Practice writing one clean sentence: “For each additional [x-unit], [y] increases/decreases by [slope value] [y-unit].” The y-intercept interpretation follows the same pattern: “When x = 0, the predicted y is [intercept].”

Difficulty Distribution

For a typical SAT test, PSDA questions distribute roughly like this:

Difficulty	Approx. Count	What Makes It Hard
Easy	5–6	Straightforward ratio, basic percent, direct table read
Medium	7–8	Multi-step percent, conditional probability, slope meaning
Hard	3–4	Statistical inference, margin of error, complex data models

The Medium bucket is where most students lose points unnecessarily. These aren’t conceptually harder — they just have more steps or require you to read the question twice. Time management matters here: if you spend 3 minutes on a medium PSDA question, you’re losing easy points elsewhere.

On the digital SAT, PSDA questions cluster in Module 2 of the Math section. If you perform well on Module 1, Module 2 tilts harder overall — meaning you’ll see more of the Hard PSDA questions. Train on hard practice questions specifically so you’re not surprised.

Expert Strategy

Start with what the question is actually asking. PSDA questions are long. Students read the setup (150 words of context about a study on coffee consumption) and by the time they hit the actual question, they’ve forgotten what to solve. Read the question stem first, then go back to the data.

Use smart numbers for abstract percent questions. Whenever a percent question doesn’t give you actual values, assign 100 to the starting quantity. This converts “what percent of the new value…” type questions from algebra problems into arithmetic problems. Takes 10 seconds, saves 2 minutes.

For statistics questions, think about what would change the mean vs. the median. The SAT tests this conceptually. Mean is sensitive to extreme values (outliers), median is not. If someone asks “a new data point is added that is far above all existing values, which measure increases more?” — the answer is always mean.

On scatterplot questions, ignore the actual data points. The question is about the line of best fit, not individual points. Unless the question specifically says “point X is above the line” (which means actual > predicted), work only with the equation.

Unit conversion: always write out your chain. Don’t do it in your head.

60 \frac{\text{miles}}{\text{hour}} \times \frac{5280 \text{ ft}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ sec}} = 88 \frac{\text{ft}}{\text{sec}}

Set it up so units cancel. If the unit you want is at the top of the final fraction, you’ve done it right.

Timing benchmark: PSDA questions should average 90 seconds each. If you’re hitting 2.5+ minutes on a question, mark it and move on. You can always return. One stuck PSDA question shouldn’t cost you three easy ones.

Common Traps

Trap 1: Percent increase ≠ the reverse of percent decrease

If a price increases by 25%, it goes from 100 → 125. To get back to 100, you need to decrease by 20% (not 25%). The SAT sets up two-step problems that exploit this asymmetry. If a value increases by $r\%$ and you want the equivalent decrease to return to original: $\frac{r}{100+r} \times 100$ .

Trap 2: Confusing “probability” with “conditional probability”

The question “what fraction of all surveyed people prefer morning?” is different from “of the students surveyed, what fraction prefer morning?” The first uses the grand total as denominator; the second uses only the student row total. Many students use the wrong denominator and both answer choices appear in the options.

Trap 3: Misreading the line of best fit as causation

SAT will sometimes ask “based on the data, which conclusion is best supported?” and include an option like “Studying more causes higher test scores.” A scatterplot shows correlation, not causation. The correct conclusion always says “associated with” not “causes.” This is a guaranteed trap in the Hard questions.

Trap 4: Adding rates directly

If Person A completes a task in 3 hours and Person B in 6 hours, their combined rate is not $\frac{1}{3} + \frac{1}{6}$ simplified wrong — it IS $\frac{1}{3} + \frac{1}{6} = \frac{1}{2}$ , meaning together they complete it in 2 hours. But the trap is when students average the times: $(3+6)/2 = 4.5$ hours. Rates add; times do not.

Trap 5: Ignoring “approximately” in data interpretation

When a graph uses a scale that makes values hard to read precisely, the SAT is testing whether you can estimate confidently. Students overthink this and second-guess themselves. If the bar clearly sits between 40 and 50 and closer to 45, pick 45. Don’t spend 90 seconds trying to read a bar graph to the nearest unit.