Ratio and Proportion Shortcuts for ASVAB Word Problems

Ratios and proportions are everywhere in arithmetic word problems: recipes, prices per pound, map scales, crews finishing a job. They're also full of quiet traps — especially when "more" means "less." Here are four shortcuts that handle almost all of them, with worked examples you can check by hand.

1. Ratios: count the parts

A class has boys and girls in the ratio 3 : 5. There are 32 students. How many are boys?

A ratio of 3 : 5 means the class splits into 3 + 5 = 8 equal parts.

1. One part: 32 ÷ 8 = 4 students.
2. Boys: 3 parts × 4 = 12.
3. Girls: 5 parts × 4 = 20. (Check: 12 + 20 = 32.)

The trap is answering with 3/5 of 32. The ratio compares boys to girls, not boys to the whole class — boys are 3 of the 8 parts, not 3 of 5.

2. Direct proportion: find the unit rate

3 pounds of apples cost $4.50. How much do 7 pounds cost?

Find the cost of one unit, then scale:

1. One pound: $4.50 ÷ 3 = $1.50.
2. Seven pounds: 7 × $1.50 = $10.50.

If the unit rate is messy, cross-multiply instead: 4.50 / 3 = x / 7, so x = 4.50 × 7 ÷ 3 = $10.50.

The same method scales a recipe:

2 cups of flour make 12 cookies. How many cups for 30 cookies?

30 is 2.5 times 12, so 2.5 × 2 cups = 5 cups.

3. Scale: multiply by the scale

On a map, 1 inch = 25 miles. Two towns are 3.5 inches apart. How far apart are they?

3.5 × 25 = 87.5 miles.

The scale is just a unit rate in disguise: 25 miles per inch.

4. Inverse proportion: multiply to get the total work

This is the trap. Some quantities go down when others go up.

6 workers can finish a job in 10 days. How long would 4 workers take, working at the same rate?

The tempting move is a direct proportion — fewer workers, fewer days. Wrong. Fewer workers take longer.

1. Total work: 6 workers × 10 days = 60 worker-days.
2. With 4 workers: 60 ÷ 4 = 15 days.

How to tell direct from inverse: ask whether increasing one quantity should increase or decrease the other.

For inverse problems, multiply to find the total (worker-days, or distance), then divide.

A one-second check for every proportion

Before choosing an answer, ask: should the answer be bigger or smaller than the number I started with? Fewer workers → more days. More pounds → more dollars. If your answer moves the wrong way, you set up the proportion backwards.

Practice it

These are the kinds of situations that arithmetic word problems are built from — and on the ASVAB you solve them without a calculator. Our free practice test includes Arithmetic Reasoning with the computer version's time limits (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.

Related: The Average Speed Trap (a rate problem that fools almost everyone) and ASVAB Word Problems: How to Translate English Into Math.

Quick answers

How do you solve a ratio word problem?

Add the parts of the ratio to get the total number of parts, divide the total by that, then multiply by the part you need. For 3 : 5 and 32 students: 32 ÷ 8 = 4, so 12 and 20.

What's the difference between direct and inverse proportion?

In a direct proportion, both quantities rise together (more pounds, more cost). In an inverse proportion, one rises as the other falls (more workers, fewer days).

How do you solve "workers and days" problems?

Multiply workers by days to get the total work, then divide by the new number of workers. 6 workers × 10 days = 60; with 4 workers, 15 days.

Is cross-multiplication allowed on the ASVAB?

Any method is fine — what matters is the answer. Just remember there's no calculator, so pick the method with the easiest arithmetic.

Sources

• What to Expect When You Take the ASVAB — officialasvab.com
• FAQs (calculators) — officialasvab.com