ASVAB Word Problems: How to Translate English Into Math

Arithmetic Reasoning is officially described as the "ability to solve arithmetic word problems." Notice what that means: the arithmetic is the easy part. The hard part is turning a sentence into the right calculation. Get the translation right and most problems become simple; get it wrong and no amount of math will save you. Here's how to translate reliably.

The translation table

These are the words that carry the math in a word problem:

The order trap: "less than"

"5 less than x" is x − 5, not 5 − x. The quantity written after "less than" is where you start, and you subtract from it. The same goes for "more than": "5 more than x" is x + 5 — the order doesn't matter for addition, which is why the trap only bites with subtraction.

A quick check: replace x with a real number. "5 less than 20" is 15. That's 20 − 5, not 5 − 20.

The percent sentence that always works

Many Arithmetic Reasoning problems hide this sentence: "What percent of A is B?" Translate it word by word:

• "What percent" → p/100
• "of" → ×
• "A" → A
• "is" → =
• "B" → B

So "What percent of 60 is 15?" becomes (p/100) × 60 = 15. Then 15 ÷ 60 = 0.25, so p = 25%.

A worked example (our own, not from the test)

Jake has 4 more than twice as many baseball cards as Maria. Together they have 31 cards. How many cards does Jake have?

Translate first, calculate second.

1. Let x be Maria's cards — the problem describes Jake in terms of Maria, so she's the unknown.
2. "Twice as many as Maria" → 2x. "4 more than that" → 2x + 4 for Jake.
3. "Together they have 31" → x + (2x + 4) = 31.
4. Combine: 3x + 4 = 31, so 3x = 27, and x = 9 (Maria).
5. Jake: 2 × 9 + 4 = 22.

Check: 9 + 22 = 31. It works.

Notice the question asks for Jake, not Maria. Stopping at x = 9 is the most common wrong answer to this kind of problem, and a multiple-choice test can easily include it as an option. Before you choose an answer, reread the last sentence of the question.

A three-step routine for every word problem

1. Read the question sentence first. Know what you're solving for before you read the details.
2. Name the unknown and write the equation before doing any arithmetic. If you can't write it, reread — the problem is in the translation, not the math.
3. Plug your answer back into the story. If the totals don't match, you've misread something.

That routine also fits the computer version's pace: on the CAT-ASVAB, Arithmetic Reasoning gives you 55 minutes for 15 scored questions, about 3.7 minutes each — enough time to translate carefully, and to check. And remember, there's no calculator on the ASVAB.

Practice

Our free practice test includes Arithmetic Reasoning with the computer version's numbers (15 questions in 55 minutes in the full version) plus the other three AFQT sections, and ends with an AFQT estimate — a practice estimate, not an official score. The questions are written by us, in the style of the test.

For the section's format and topics, see Arithmetic Reasoning Practice Test. For three time-saving techniques, see 3 Arithmetic Reasoning Shortcuts That Save Real Minutes.

Quick answers

What does "of" mean in math word problems?

Usually multiply, especially with fractions and percents: "half of 40" is ½ × 40 = 20.

Is "5 less than x" x − 5 or 5 − x?

x − 5. Start with x and take 5 away. Test it with a number: 5 less than 20 is 15.

How do I solve "what percent of A is B"?

Divide B by A and multiply by 100. What percent of 60 is 15? 15 ÷ 60 = 0.25 = 25%.

Can I use a calculator on ASVAB word problems?

No. Calculators aren't allowed on any version of the ASVAB.

Sources

• What to Expect When You Take the ASVAB — officialasvab.com
• Sample Questions — officialasvab.com