ASVAB Arithmetic Reasoning: 5 Word Problems Solved Step by Step (Victorville & Hesperia)

Arithmetic Reasoning is the ASVAB section that scares most people. It is not hard math. It is everyday math hidden inside a story. Once you learn to pull the numbers out of the story, the questions get much easier.

Below are five real-style word problems, solved one step at a time, the way we teach them at US Elite Mathematics Tutoring in Hesperia and Victorville. Try each one first. Then check the steps.

Remember: no calculator on the ASVAB. Every step below can be done by hand.

The 3-step method for every word problem

• 1. Find the question. What exactly are they asking for? Write it down.

• 2. Pull out the numbers. Ignore the story. Keep only what you need.

• 3. Pick the operation, then check. Does your answer make sense in real life?

Problem 1 — Percent off

A jacket costs $80. It is on sale for 25% off. What is the sale price?

Step 1: 25% of 80 = 0.25 × 80 = 20.

Step 2: 80 − 20 = 60.

Answer: $60. Shortcut: 25% off means you pay 75%. 0.75 × 80 = 60. Same answer, one step.

Watch out: many people stop at $20. That is the discount, not the price. Always re-read the question.

Problem 2 — Distance, rate and time

A truck drives 210 miles in 3.5 hours. What is its average speed?

Use: speed = distance ÷ time.

210 ÷ 3.5 is easier as 420 ÷ 7 (double both numbers). 420 ÷ 7 = 60.

Answer: 60 miles per hour. Check: 60 × 3.5 = 210. ✔

Problem 3 — Ratios

A group of 40 recruits has men and women in a ratio of 3 to 2. How many women are in the group?

Step 1: Add the ratio parts. 3 + 2 = 5 parts.

Step 2: One part = 40 ÷ 5 = 8 people.

Step 3: Women = 2 parts = 2 × 8 = 16.

Answer: 16 women. Check: men = 3 × 8 = 24, and 24 + 16 = 40. ✔

Problem 4 — Averages

Your first three test scores are 82, 90 and 76. What score do you need on the fourth test to average 85?

Step 1: To average 85 on 4 tests, the total must be 85 × 4 = 340.

Step 2: You already have 82 + 90 + 76 = 248.

Step 3: 340 − 248 = 92.

Answer: 92. This "total first" trick works on every missing-average question.

Problem 5 — Simple interest

You put $1,200 in an account that pays 5% simple interest per year. How much interest do you earn in 3 years?

Use: interest = principal × rate × time.

1,200 × 0.05 = 60 per year. 60 × 3 = 180.

Answer: $180. Watch out: the question asks for the interest, not the new balance ($1,380). Read the last line twice.

The pattern behind all five

Notice what happened. Every problem used one simple formula, and every mistake came from answering a different question than the one asked. That is why ASVAB math scores often jump fast with the right practice: the math is not new, the habits are.

Arithmetic Reasoning and Mathematics Knowledge both count toward your AFQT score, which affects whether you qualify and which jobs you can choose. Strong math here opens doors.

Watch more worked problems

Mr. T works through ASVAB, SAT, CSET and Algebra problems on the US Elite YouTube channel. Watch the videos on our YouTube channel.

Frequently asked questions

Can I use a calculator on the ASVAB?

No. That is why we practice clean hand methods like the ones above.

What math is on the ASVAB?

Arithmetic Reasoning (word problems with percents, rates, ratios, averages and money) and Mathematics Knowledge (algebra, geometry and number rules).

Do you offer ASVAB math tutoring near Victorville and Hesperia?

Yes. We tutor one-on-one in person in Hesperia, Victorville, Apple Valley and Oak Hills, and online anywhere in the US. No office visit needed: we come to you, or you join from home.

Is the first session really free?

Yes. In your free first session we find exactly which question types are costing you points and give you a clear study plan. You keep the plan whether you enroll or not.

Ready to raise your ASVAB math score?

Our goal is simple: to be the best math help in the High Desert. Your first session is FREE, so there is nothing to lose. Bring the problems that stump you, and we will fix them together.

Call or text 909-780-9495 or book at www.uselitemathematicstutoring.org.

US Elite Mathematics Tutoring • 16117 Main Street, Hesperia, CA 92344 • tmalik@uselitemathematicstutoring.org