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No calculator on the ASVAB? Here's the math that replaces it

You get scratch paper, a pencil and more time per question than you think. Seven shortcuts that cover most of Arithmetic Reasoning, worked step by step.

5 min read5 practice questions

On this page
  1. Why the ASVAB doesn't allow calculators
  2. Seven shortcuts that cover most of Arithmetic Reasoning
  3. Scratch work that doesn't trip you up
  4. Try it: five Arithmetic Reasoning questions
  5. Quick answers
  6. Sources

Short answer: no calculator is allowed on the ASVAB, on the computer, on paper or at home on the PiCAT. You work on scratch paper with a pencil. On the computer test, Arithmetic Reasoning gives you 55 minutes for 15 questions, about 3 minutes 40 seconds each, which is plenty of time for the hand methods below.

Why the ASVAB doesn't allow calculators

The official ASVAB site explains it. School tests measure what you've learned, so a calculator can make sense there. The ASVAB is an employment test: it measures whether you can apply what you know to problems a job might hand you, and some jobs need you to work numbers by hand. So that's what it tests.

The good news is that ASVAB math isn't advanced. Arithmetic Reasoning is word problems about money, percents, rates, ratios and time. Mathematics Knowledge is high-school algebra and geometry. Questions are written to be worked by hand, so when the numbers get ugly, it usually means there's a simpler setup you haven't spotted.

Seven shortcuts that cover most of Arithmetic Reasoning

Build any percent from 10% and 5%

Ten percent is the number with the decimal point moved one place left. Half of that is 5%. Most percents on the test are a few of these pieces added together.

Find 15% of 80

  1. 10% of 80 is 8: move the decimal point one place left.
  2. 5% is half of 10%: 4.
  3. 15% = 8 + 4 = 12

Percent change divides by the original

The most common trap on the test. A change is always compared with where you started, so the same $10 is a different percent going up than coming down.

A price rises from $40 to $50. By what percent?

  1. The change is 50 - 40 = $10.
  2. Divide by the original price, $40: 10 ÷ 40 = 1/4.
  3. 1/4 = 25% increase (not 20%)

Going back down from $50 to $40 is a 10 ÷ 50 = 20% decrease, because now $50 is the original.

Work rates add; times don't

When two people or machines work together, add how much each gets done per hour, never their times. Then flip the total rate to get the time.

3.0hours

1/4 + 1/12 = 1/3 of the tank per hour

Pipe A fills the tank in 4 hours and pipe B in 12. Open together they take neither 8 hours nor 16: their rates add, 1/4 + 1/12 = 1/3 of a tank per hour, so 3 hours.

For exactly two workers there's a shortcut: multiply the two times and divide by their sum. Here that's (4 × 12) ÷ (4 + 12) = 48 ÷ 16 = 3 hours. Sanity check: working together must take less time than the faster one alone.

Round-trip speed isn't the average of the speeds

Average speed is total distance divided by total time. A slow leg eats more time, so it pulls the average down more than a fast leg pulls it up.

Drive 60 miles out at 30 mph and back at 60 mph. Average speed?

  1. Out: 60 ÷ 30 = 2 hours. Back: 60 ÷ 60 = 1 hour.
  2. Total: 120 miles in 3 hours.
  3. 120 ÷ 3 = 40 mph (not 45)

Ratios: count the parts

A ratio like 3 to 5 splits a total into 3 + 5 = 8 equal parts. Find the size of one part and everything else follows.

Split 64 in the ratio 3 to 5

  1. 3 + 5 = 8 parts.
  2. One part is 64 ÷ 8 = 8.
  3. 3 × 8 = 24 and 5 × 8 = 40

Dividing by a fraction means multiplying by its flip

Turn the second fraction upside down and multiply. It also helps to ask the question in words: how many three-quarters fit into 6?

Find 6 ÷ 3/4

  1. Flip 3/4 to 4/3.
  2. 6 × 4/3 = 24/3.
  3. 24 ÷ 3 = 8

Averages: work with the total

An average times the count gives the total. Questions that ask what score you need next are really asking how many points are missing from that total.

Scores of 80, 90 and 82. What's needed on test four to average 85?

  1. An 85 average over four tests is 4 × 85 = 340 points.
  2. So far: 80 + 90 + 82 = 252.
  3. 340 - 252 = 88

Scratch work that doesn't trip you up

  • Write what you're solving for first. Many misses answer a different question than the one asked, like the discount instead of the sale price.
  • Keep the units next to every number. Hours, minutes, dollars and gallons don't mix.
  • Estimate before you compute. If three items cost about $50 each, the answer is near $150, and you can rule out choices that aren't.
  • Make friendly numbers. 25 × 16 is 100 × 4 = 400. Multiplying by 5 is multiplying by 10 and halving.
  • Check the answer makes sense. A sale price above the original, or a combined time longer than one worker alone, means a setup went wrong.

Try it: five Arithmetic Reasoning questions

Use scratch paper, no calculator. Each answer comes with a worked explanation.

Quick check 5 questions

  1. ARArithmetic ReasoningAFQT1 of 5

    A field jacket normally sells for $80 and is marked 25% off. What is the sale price?

    Show answer

    Answer: B. $60

    25% of 80 is 0.25 × 80 = 20, so the price drops to 80 − 20 = 60. Shortcut: paying after 25% off means paying 75%, and 0.75 × 80 = 60.

  2. ARArithmetic ReasoningAFQT2 of 5

    A convoy must travel 180 miles at an average speed of 45 miles per hour. How long will the trip take?

    Show answer

    Answer: B. 4 hours

    Time equals distance divided by speed: 180 ÷ 45 = 4 hours. Keep the triangle in mind: distance = speed × time, so time = distance ÷ speed and speed = distance ÷ time.

  3. ARArithmetic ReasoningAFQT3 of 5

    A mess-hall recipe uses flour and sugar in a 3-to-2 ratio. If a batch uses 12 cups of flour, how much sugar does it need?

    Show answer

    Answer: D. 8 cups

    Set up the proportion 3/2 = 12/x. Cross-multiply: 3x = 24, so x = 8. Each 'part' is 4 cups because 12 cups of flour is 3 parts.

  4. ARArithmetic ReasoningAFQT4 of 5

    A mechanic earns $18 per hour for a 40-hour week and time-and-a-half for overtime. How much does he earn in a week with 5 overtime hours?

    Show answer

    Answer: A. $855

    Regular pay: 40 × 18 = 720. Overtime rate: 18 × 1.5 = 27, and 5 × 27 = 135. Total: 720 + 135 = 855.

  5. ARArithmetic ReasoningAFQT5 of 5

    A rectangular training field measures 40 yards by 60 yards. How much fencing is needed to enclose it completely?

    Show answer

    Answer: C. 200 yards

    Perimeter of a rectangle is 2 × (length + width) = 2 × (40 + 60) = 200 yards. Multiplying 40 × 60 gives 2,400, which is the area in square yards, not the fence length.

Mathematics Knowledge follows the same no-calculator rule. Its free practice test covers equations, exponents, geometry and probability.

Quick answers

Can you use a calculator on the ASVAB?

No, on any version: at a MEPS, at a test site or at home on the PiCAT. The test is designed to measure whether you can do the math by hand.

What kind of math is on the ASVAB?

Arithmetic Reasoning is word problems: percents, rates, ratios, averages, money and time. Mathematics Knowledge is high-school math: algebra, geometry, exponents, roots and probability. Both count toward your AFQT.

Do you get scratch paper on the ASVAB?

Yes. On the computer test, if you need more scratch paper or another pencil, you press the HELP key, and the subtest clock stops while you get it.

How much time do you get per math question?

On the computer test, about 3 minutes 40 seconds per Arithmetic Reasoning question (15 in 55 minutes) and about 2 minutes per Mathematics Knowledge question (15 in 31 minutes).

Sources