SHSAT Word Problems: The Math Questions That Trip Up Everyone
Here is the mistake most students make when preparing for SHSAT math: they study "word problems" as if it is a separate topic, like algebra or geometry. It is not. Word problems are a delivery method. They are the packaging that wraps around algebra, ratios, percentages, geometry, and statistics.
On the actual test, roughly half of the 57 math questions present their content as word problems. You might get an algebra equation handed to you directly, or you might get a paragraph about a store selling discounted sneakers that requires you to set up the same algebra equation yourself. The math is identical. The challenge is translation.
Our mock exam data confirms this pattern. The dedicated "Word Problems" category contains 34 questions, but word-problem formatting appears across algebra (148 questions), ratios and proportions (114 questions), statistics and probability (68 questions), and every other category. If you cannot translate English into math, you cannot pass the SHSAT math section. Period.
Why Word Problems Are the Real Test
Multiple-choice math with numbers and symbols already on the page tests computation. Can you solve 3x + 7 = 22? Most SHSAT students can.
Word problems test comprehension first and computation second. Can you read "Maria has 7 more than three times the number of books that James has" and turn it into 3x + 7? That translation step is where points are won and lost.
Grid-in questions make this even higher stakes. Our mock exams contain 50 grid-in questions, and word problems lead the pack: 13 of 50 grid-ins (26%) are pure word problems. With no answer choices to eliminate or back-solve from, you either translate correctly and compute accurately, or you get zero points. For more on grid-in strategy, see our complete grid-in guide.
The 3-Step Translation Method
Every word problem, regardless of topic, follows the same solving process. Master these three steps and you have a framework for any word problem on the test.
Step 1: Identify What Is Being Asked
Read the last sentence first. That is where the question lives. Before you process any of the given information, know what you are solving for.
This sounds simple, but skipping this step is the number one cause of wrong answers on word problems. Students read from top to bottom, start calculating as soon as they see numbers, and end up solving for the wrong thing.
Example: "A store sells notebooks for $3 each and pens for $1.50 each. Marcus buys 4 notebooks and some pens. He spends $18 total. How many pens did Marcus buy?"
The question is asking for the number of pens. Not the total cost. Not the cost of notebooks. The number of pens. Write it down: "Find: number of pens."
Step 2: Define Your Variables
Assign a letter to the unknown quantity. If the question asks for the number of pens, let p = number of pens.
If there are multiple unknowns, try to express them in terms of one variable. "James has twice as many books as Maria" means if Maria has x books, James has 2x. You do not need two separate variables.
Step 3: Translate Words to Equations
This is the core skill. Use the word-to-math dictionary:
| English | Math |
|---|---|
| "more than" or "increased by" | + |
| "less than" or "decreased by" | - |
| "times" or "product of" | x |
| "per" or "each" or "for every" | ÷ |
| "is" or "equals" or "was" | = |
| "of" (with fractions/percentages) | x |
| "what number" or "how many" | variable (x, n, etc.) |
Back to our example:
- 4 notebooks at $3 each = 4 x 3 = $12
- p pens at $1.50 each = 1.50p
- Total = $18
- Equation: 12 + 1.50p = 18
- Solve: 1.50p = 6, so p = 4
Marcus bought 4 pens. The translation, not the arithmetic, was the hard part.
The 4 Traps That Cost Students Points
Trap 1: Solving for the Wrong Value
The question asks for 2x + 1, but you solve for x and pick that answer. This is devastatingly common on the SHSAT because answer choices are designed to include intermediate values.
Example: "If 3x + 5 = 20, what is the value of 6x + 10?"
Students solve 3x + 5 = 20, get x = 5, and look for 5 in the answer choices. But the question asks for 6x + 10. The answer is 40. (Or notice that 6x + 10 = 2(3x + 5) = 2(20) = 40, no need to find x at all.)
Prevention: After solving, re-read the question. Does your answer match what was asked? Circle the exact quantity the question requests before you start solving.
Trap 2: Extra Information
SHSAT word problems routinely include numbers that are irrelevant to the solution. They are there to distract.
Example: "A classroom has 28 students. 15 are girls. The teacher brings 3 boxes of supplies, each containing 12 items. If each student receives the same number of items, how many items does each student receive?"
The number 15 (girls) is irrelevant. You need: 3 x 12 = 36 items, divided by 28 students = 36/28. But students who latch onto "15 girls" might try to calculate something with it.
Prevention: After reading the question (Step 1), go back through the information and mark which numbers you actually need. Cross out the rest mentally.
Trap 3: Unit Mismatches
The problem gives time in minutes, but the question asks for hours. Or the problem uses inches, but the answer choices are in feet. Or a rate is given "per hour" but the time period in the problem is in minutes.
Example: "A car travels at 60 miles per hour. How far does it travel in 45 minutes?"
Students who multiply 60 x 45 get 2,700, which is absurd. The correct calculation: 45 minutes = 0.75 hours, so 60 x 0.75 = 45 miles.
Prevention: Before any calculation, check units. Write them next to every number. If they do not match, convert before computing.
Trap 4: Not Reading "At Least," "At Most," and "No More Than"
These qualifier words change equations into inequalities, and they also affect which answer is correct when multiple choices are close.
- "At least 5" means 5 or more (≥ 5)
- "At most 5" means 5 or fewer (≤ 5)
- "No more than" means the same as "at most"
- "More than 5" means greater than 5 (> 5, not including 5)
Prevention: Underline qualifier words. They are easy to miss on a first read but completely change the problem.
Word Problems by Math Topic
Different math topics produce different types of word problems. Here is what to expect across our 22 math subtopics.
Rate and Speed Problems (60 questions)
The classic: "If Train A leaves at 8 AM going 60 mph and Train B leaves at 9 AM going 80 mph..."
The formula: Distance = Rate x Time (d = rt)
The key insight: When two objects are moving, decide whether they are moving toward each other (add rates), away from each other (add rates), or in the same direction (subtract rates).
Common variation: "Work rate" problems. "If Alex can paint a room in 4 hours and Brenna can paint it in 6 hours, how long does it take them together?" Here, rates are fractions of the job: 1/4 + 1/6 = 5/12 of the job per hour, so total time = 12/5 = 2.4 hours.
Percentage Problems (60 questions)
Percentage word problems dominate retail scenarios: discounts, tax, tips, markups, and percentage change.
The formula: Part = Percentage x Whole, or equivalently: Percentage = Part / Whole
Common trap: Percentage increase vs. percentage of. "The price increased by 20%" means new price = 1.2 x old price. "The price is 20% of the original" means new price = 0.2 x old price. These are very different.
Successive percentages: A 20% discount followed by a 10% discount is not a 30% discount. It is: 0.8 x 0.9 = 0.72, or a 28% total discount.
Ratio and Proportion Problems (60 questions)
"The ratio of boys to girls is 3:5. If there are 24 boys, how many girls are there?"
The method: Set up a proportion. 3/5 = 24/x. Cross-multiply: 3x = 120, x = 40.
Common trap: Confusing "ratio of A to B" with "ratio of A to total." If boys to girls is 3:5, boys to total is 3:8, not 3:5.
Algebra Word Problems (148 questions in mock exams)
These are the broadest category. Any scenario that requires setting up and solving an equation falls here.
Typical patterns:
- Age problems: "Maria is 3 years older than twice James's age..."
- Consecutive integer problems: "The sum of three consecutive odd numbers is 87..."
- Mixture problems: "A solution is 40% acid. How much water must be added..."
The approach: Always the 3-step method. Identify what is asked. Define variables. Translate and solve.
For a complete breakdown of every algebra subtopic, see our SHSAT math study guide.
Grid-In Word Problems: No Safety Net
Of the 50 grid-in questions across our 10 mock exams, 13 are pure word problems. That is 26% - the single largest grid-in category.
Why this matters: on multiple-choice questions, you can back-solve by plugging answer choices into the word problem. On grid-ins, that option disappears. You must translate the words into math, solve correctly, and enter the exact numerical answer.
Grid-in specific tips for word problems:
- Double-check your answer against the question. Did they ask for x or 2x?
- Check units. If the answer should be in hours, make sure you did not leave it in minutes.
- If you get a fraction, do not convert to a mixed number. Enter it as an improper fraction (e.g., 7/2, not 3 1/2).
- Do not enter units or labels. Just the number.
For the full guide to grid-in format and rules, see our grid-in questions guide.
A Word Problem Practice Plan
Phase 1 - Translation drills (Week 1-2): Take 10 word problems per day. Do not solve them. Instead, practice only the translation: identify what is asked, define variables, write the equation. Check whether your equation matches the solution approach. This isolates the skill that actually matters.
Phase 2 - Solve by topic (Week 3-6): Work through word problems organized by math topic. Our targeted practice lets you filter by subtopic, so you can focus on rate problems one day, percentage problems the next, and ratio problems after that. Do 15-20 per session.
Phase 3 - Mixed practice under time (Week 7+): Take full mock exams and track your word problem accuracy across all categories. Our 10 mock exams contain 1,140 math questions total, with word-problem formatting spread across every section. Pay special attention to grid-in word problems, where precision matters most.
The difficulty ramp: Start with easy-difficulty questions (roughly 20 per subtopic in our bank), move to medium (29 per subtopic), and save hard (11 per subtopic) for the final weeks of prep. See our study plan guide for how to structure this progression over 3, 6, or 12 months.
The Translation Mindset
Word problems are not a math topic. They are a reading skill applied to math. Students who are strong readers but struggle with word problems usually have a translation problem, not a computation problem. Students who are strong at computation but weak at word problems have the same issue from the other direction.
The fix is the same for both: practice the 3-step translation method until it becomes automatic. Read the question first. Define your unknowns. Convert English to math. Then, and only then, start computing.
The 2025 SHSAT tested 25,933 students, and only 15.5% received offers. In a test that competitive, the students who earn offers are the ones who do not lose points to careless translation errors. Master word problems, and you remove one of the biggest sources of lost points on the math section.
For the broader view of how math scoring works and why maximizing your math score might matter more than you think, read our scoring strategy guide.
