🔢 Word Problems with Whole Numbers

Part 1 of 7 — Word Problems on the AR Subtest

Topic Overview

What these questions look like

The official description of Arithmetic Reasoning (AR) is short: "Ability to solve basic arithmetic word problems." Most AR items are a little story of two to four sentences (a paycheck, a supply order, a shift schedule, a room that needs new flooring) followed by one question and four answer choices.

The arithmetic is usually just adding, subtracting, multiplying and dividing. What makes AR feel hard is the reading:

• deciding which operation the story is describing,
• doing two or three steps in the right order,
• and answering the question that was actually asked, in the units it asked for.

This topic is about whole numbers and whole-dollar money. Fractions, percents, ratios and averages each have their own topic in this unit.

🔢 Word Problems with Whole Numbers

Part 2 of 7 — Turning Words into Operations

Four actions, four operations

Every one-step word problem does one of four things with its numbers. Before you look for key words, ask: what is the story doing?

Set up the number sentence before you compute

Write the problem as a short number sentence, with a word standing in for the answer. This takes ten seconds and prevents most operation mistakes.

Worked Example 1. Six friends share a $420 cabin rental equally. How much does each one pay?

• The story splits $420 into 6 equal shares.
• Number sentence: $420 \div 6 = \text{one share}$
• Compute: $420 \div 6 = 70$, so each pays $70.
• Check: $6 \times 70 = 420$. ✓

Now flip it: each of 6 friends pays $70; what is the total rent? The story now repeats $70 six times: $6 \times 70 = 420$, so $420. The word "each" appears in both versions, but the operations are opposite. That is why the action matters more than any single word.

🔢 Word Problems with Whole Numbers

Part 3 of 7 — Multi-Step Problems and Order of Operations

A multi-step problem is a chain of one-step problems

Most AR questions take two to four steps. Each step is one of the four actions from Part 2. The answer to one step becomes a number in the next one.

The plan is always the same:

1. What does the question want? (Last sentence, with its unit.)
2. What do I know? (The numbers in the story.)
3. What is missing in between? (The intermediate results you must find first.)

Label every intermediate result

On scratch paper, write a word next to each number you find. When you reach the end, you can see at a glance which number answers the question, and you won't pick a subtotal by mistake.

Worked Example 1 — Buying and making change. A soldier buys 3 T-shirts at $14 each and 2 pairs of socks at $6 each. She pays with a $100 bill. How much change does she get?

Her change is $46. Estimate check: she spent a bit more than $50, so the change should be a bit less than $50. ✓ Notice that $54 (the total spent) is sitting right there on the scratch paper. It answers a different question.

🔢 Word Problems with Whole Numbers

Part 4 of 7 — Measurement: Units, Perimeter and Area

The conversions you need to know cold

The test expects you to know these. Nobody will give them to you.

Which way to convert

• Big unit → small unit: multiply. There are more of the small units. 3 hours 25 minutes is $3 \times 60 + 25 = 205$ minutes.
• Small unit → big unit: divide. There are fewer of the big units. 78 inches is $78 \div 12 = 6$ remainder 6, so 6 feet 6 inches.

Reasonableness: after converting to a smaller unit, the number should get bigger. If 3 hours became 20 "minutes", you divided when you should have multiplied.

Key Fact: Before you compute, circle the unit in the last sentence. If the question asks for minutes and the story gives hours, the conversion is one of the steps.

🔢 Word Problems with Whole Numbers

Part 5 of 7 — Remainders, Rounding Up and Estimation

One division, three different answers

When a division doesn't come out even, the remainder forces a decision. The story decides, not the arithmetic.

A supply clerk has 230 bandage rolls. Every first-aid kit uses 12 rolls, and the rolls ship in boxes of 12.

$230 \div 12 = 19 \text{ remainder } 2 \qquad (12 \times 19 = 228, \; 230 - 228 = 2)$

Same numbers, three correct answers to three different questions. That is why you read the last sentence first.

🔢 Word Problems with Whole Numbers

Part 6 of 7 — Test Strategy and Common Traps

The six traps the wrong answers are built from

AR answer choices are designed around predictable mistakes. Once you know them, you'll recognize them on sight.

Key Fact: If your answer matches a choice on the first try, that's good, but it doesn't prove you're right. The trap answers match choices too. The final check is what separates them.

🔢 Word Problems with Whole Numbers

Part 7 of 7 — Mixed Mastery Set

Put it all together

This set mixes every skill from the topic, in roughly the order a real AR subtest would build: a few quick ones, a solid middle, then a few that take more steps.

Work each one the way you would at MEPS: last sentence first, a number sentence, units on every line, an estimate, and a final check. Aim for about 2 to 3 minutes per problem, faster on Set A.