SSAT-MIDDLE-LEVEL-QUANTITATIVE • QUANTITATIVE

Identify Relevant Information and Plan a Solution Path

Learn how to sort through word problems, pick out what matters, and build a step-by-step plan to reach the answer.

Why Do We Need a Plan?

People have been solving math problems for thousands of years. But here is something interesting: the best problem solvers are not always the fastest at arithmetic. They are the best at organizing information before they even start calculating. Throughout history, mathematicians have developed strategies for breaking problems into smaller, more manageable pieces.

~300 BC
Euclid's Elements
The Greek mathematician Euclid wrote one of the first math textbooks. He showed that every proof should start by listing exactly what you know and what you need to find.
~825 AD
Al-Khwarizmi's Algorithm
The Persian scholar Al-Khwarizmi created step-by-step methods for solving equations. The word "algorithm" (a set of steps to solve a problem) comes from his name.
1945
Pólya's Problem-Solving Steps
Mathematician George Pólya published "How to Solve It," a book that laid out four clear steps: understand the problem, make a plan, carry out the plan, and look back.
Today
Standardized Test Strategy
Modern tests like the SSAT give you word problems loaded with details. Your job is to separate what matters from what does not, then pick the right operations to reach the answer.

The big question these thinkers all tried to answer is the same one you face on the SSAT: How do I turn a confusing problem into a clear path to the answer? That is exactly what this lesson will teach you.

Core Principles of Problem Solving

Before you do any math, you need a game plan. Think of it like packing for a trip. You would not throw everything in your closet into a suitcase. You would figure out where you are going, what the weather is like, and then pack only what you need. Problem solving works the same way.

1

Read the Whole Problem

Read the problem all the way through before doing anything. Get the big picture first. Ask yourself: what is this problem about?
2

Identify What You Need to Find

Find the question being asked. Circle or underline it. This is your destination — everything you do should lead here.
3

Pull Out the Key Facts

List the numbers and facts that connect to the question. Ignore extra details that do not help you get to the answer.
4

Choose Your Operations

Decide which math operations (addition, subtraction, multiplication, division) will get you from the given facts to the answer.
5

Check Your Answer

After solving, ask: does this answer make sense? Is it the right size? Did I answer the actual question that was asked?
KEY TAKEAWAY
Think of a word problem like a recipe. The question is the dish you want to cook. The given numbers are your ingredients. Extra information is like stuff in your fridge that you do not need for this recipe — just leave it on the shelf. Once you pick the right ingredients, you follow the steps (operations) in the right order to cook up the answer.

Seeing the Problem-Solving Process

The diagram below shows the five-step process as a flowchart. Notice how you start at the top by reading the problem, then move down step by step. If your answer does not make sense at the end, the arrow loops you back to check your work.

Follow the five rounded boxes from top to bottom. The dashed red arrow on the right shows what to do if your answer seems wrong — loop back and recheck your facts and operations.

This flowchart is your mental checklist. On the SSAT, you will not have time to draw it on paper for every question. But after practicing, these steps will become automatic. You will naturally read the question, spot the key facts, pick the right operation, and check your work — all in under a minute.

Translating Words into Math

One of the trickiest parts of word problems is figuring out which math operation to use. Certain signal words (words that hint at an operation) hide inside the sentences. Learning to spot them is like learning a secret code.

ADDITION SIGNALS
total = part₁ + part₂ + …
Look for words like: sum, total, altogether, combined, in all, increased by, more than
SUBTRACTION SIGNALS
difference = larger − smaller
Look for words like: difference, fewer, less than, remaining, left over, decreased by, how many more
MULTIPLICATION SIGNALS
product = quantity × rate (or groups × items per group)
Look for words like: times, each, per, every, of, double, triple, product
DIVISION SIGNALS
quotient = total ÷ number of groups
Look for words like: split, share equally, divided by, per, ratio, average, out of
⚠️ Watch Out!
The phrase "less than" reverses the order. "5 less than 12" means 12 − 5, not 5 − 12. Always think about what the sentence is actually saying.

Sorting Relevant from Extra Information

SSAT problems often include numbers or facts that you do not need. They are there to test whether you can tell the difference between relevant information (facts that help you answer the question) and extra information (facts that do not connect to the question). Let's look at a sample problem and sort its details.

📝 Sample Problem
Maria is 12 years old. She bought 3 notebooks at $4 each and 2 pens at $2 each. She paid with a $20 bill. How much change did she receive?
The left column shows the three facts we need: the notebooks, pens, and amount paid. The right column shows the one extra fact — Maria's age — which has nothing to do with calculating change. The bottom bar shows the solution plan built from only the relevant facts.

Here is a quick test you can use for any fact in a problem: ask yourself, "Does this number or detail connect to the question?" If the answer is no, set it aside. If the answer is yes, write it down and figure out how it fits into your solution path.

Worked Example: Full Problem Walkthrough

🚂 Problem
A train travels at 60 miles per hour. The train has 8 cars and left the station at 9:00 AM. How far will the train have traveled by 11:30 AM?
Step-by-Step Solution
1
Step 1 — Read and Find the QuestionThe question asks: "How far will the train have traveled by 11:30 AM?" So we need to find a distance.
Goal: find the distance traveled
2
Step 2 — Identify Relevant InformationRelevant: speed = 60 miles per hour, departure time = 9:00 AM, arrival time = 11:30 AM. Extra: the train has 8 cars — this does not affect distance.
Key facts: 60 mph, 9:00 AM to 11:30 AM
3
Step 3 — Choose OperationsTo find distance, we use: distance = speed × time. First we need to figure out how much time passed. From 9:00 AM to 11:30 AM is 2 hours and 30 minutes, which equals 2.5 hours.
Time = 2.5 hours
4
Step 4 — SolveDistance = 60 × 2.5. We can break this into easier pieces: 60 × 2 = 120 and 60 × 0.5 = 30. Then 120 + 30 = 150.
Distance = 150 miles
5
Step 5 — CheckDoes 150 miles make sense? At 60 mph, you travel 60 miles in one hour and 120 miles in two hours. Half an hour more adds 30 miles. So 120 + 30 = 150 miles. ✓ It checks out.
Answer confirmed: 150 miles

Notice how we never used the fact that the train has 8 cars. That detail was extra information placed there to distract you. On the SSAT, always be on the lookout for numbers that have nothing to do with the question.

Common Mistakes and How to Avoid Them

Even strong math students lose points by falling into common traps. Here is a comparison of what can go wrong and how to stay on track.

Four common mistakes and their fixes
Common MistakeWhy It HappensHow to Fix It
Using extra information in your calculationYou grab every number in the problem without asking if it connects to the questionBefore calculating, label each fact as "relevant" or "extra"
Choosing the wrong operationYou do not look for signal words or think about what the question is really askingReread the question and match key words to operations (see Section 4)
Answering a different question than what was askedYou solve for one thing when the question asks for something else (e.g., finding total cost when the question asks for change)Underline the actual question. After solving, reread it to make sure you answered it.
Skipping the check stepYou rush to the next problem without verifying your answer is reasonableTake 5 seconds to ask: is this answer too big, too small, or about right?
KEY TAKEAWAY
On the SSAT, wrong answer choices are designed to match common mistakes. If you use extra information, you will often get a number that is one of the wrong choices. That is not a coincidence — the test makers predict the errors students make. Following your plan protects you from these traps.

Connecting to Harder Problem Types

The planning strategy you just learned works for every kind of SSAT math problem. As problems get harder, the planning step becomes even more important. Here is how the same five steps apply to more advanced problem types you will encounter.

How planning applies to basic and advanced SSAT problems
Problem TypeBasic Version (This Lesson)Advanced Version (What's Next)
Arithmetic word problemOne or two operations, one piece of extra infoThree or more operations, multiple extra details
Geometry problemFind area using given length and widthFind area of a combined shape where you must first calculate a missing side
Rate / distance / timeSingle trip at one speedTwo legs of a trip at different speeds; find average speed
Data interpretationRead one value from a chartCompare multiple values and calculate percent change

No matter how complex a problem gets, your first move is always the same: find the question, gather the relevant facts, ignore the rest, and choose your operations. The more you practice this habit now, the more naturally it will come when the problems get tougher.

Practice Problems

Try each problem on your own before reading the answer. For every problem, start by identifying the question, pulling out the relevant facts, and choosing your operations.

PROBLEM 1CONCEPTUAL
A problem says: "Jake is 11 years old. He has 5 red marbles and 8 blue marbles. How many marbles does he have in all?" Which piece of information is NOT needed to solve this problem? (A) Jake has 5 red marbles (B) Jake is 11 years old (C) Jake has 8 blue marbles (D) Jake has marbles of two colors (E) The total number of marbles
PROBLEM 2BASIC CALCULATION
Emma practiced piano for 45 minutes on Monday, 30 minutes on Tuesday, and 50 minutes on Wednesday. Her piano teacher is 28 years old. What is the total number of minutes Emma practiced? (A) 95 minutes (B) 105 minutes (C) 123 minutes (D) 125 minutes (E) 153 minutes
PROBLEM 3INTERMEDIATE
A rectangular garden is 12 feet long and 8 feet wide. A fence costs $5 per foot. The garden has 3 rows of tomatoes. How much will it cost to build a fence around the entire garden? (A) $96 (B) $120 (C) $160 (D) $200 (E) $480
PROBLEM 4APPLIED
A school is planning a field trip. There are 126 students going. Each bus holds 42 students. The bus ride is 35 miles long and the bus company charges $210 per bus. How much will the school pay for buses in total? (A) $210 (B) $420 (C) $630 (D) $735 (E) $5,292
PROBLEM 5CRITICAL THINKING
A store sells boxes of colored pencils. Small boxes hold 12 pencils and cost $6. Large boxes hold 36 pencils and cost $15. The store has been open for 4 years. Mrs. Lee needs at least 100 colored pencils. What is the least amount of money she can spend to get at least 100 pencils? (A) $42 (B) $45 (C) $48 (D) $50 (E) $54

Lesson Summary

Every SSAT word problem can be tackled with a clear five-step process: read the whole problem, find the question, pull out the key facts while ignoring extra information, choose the right operations using signal words, and check that your answer makes sense. This process works whether the problem involves arithmetic, geometry, rates, or data.

Remember that wrong answer choices are often built from common mistakes like using extra numbers or picking the wrong operation. By following your plan, you avoid those traps. Practice sorting information and choosing operations on simple problems first. As this becomes a habit, you will be ready to apply it to the trickiest problems the SSAT throws at you.

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