Reading a Word Problem

Arithmetic Reasoning does not test arithmetic. The arithmetic in a typical question is two operations on numbers under a hundred, which you could do in middle school. What it tests is whether you can read a paragraph written by someone who is deliberately not making it easy, and come out the other side with the right setup.

That is a different skill, and it is trainable in a way that "being good at math" is not.

Read the last sentence first

The question lives at the end. Everything above it is supply.

Reading the question before the story changes what you notice while you read the story. If you know you need a per-hour figure, the words "per week" stand out when you reach them. If you read front to back, you absorb everything with equal weight, get to the end, and have to go back up anyway.

So: eyes to the last sentence, read it, then read the whole thing from the top. That is two passes, and on this subtest you have the time.

While you read, three questions run in the background:

1. What am I solving for, and in what unit? Dollars, hours, miles, people, percent. Write the unit down if you are writing anything down.
2. Which numbers matter? Not all of them will.
3. Is the answer bigger or smaller than the numbers I was given? This is the cheapest sanity check available and it catches a surprising share of errors before you make them.

The question under the question

Here is the shape that costs more points than any other on the subtest.

A crew of four paints a barracks in 6 hours. Working at the same rate, how much longer would it take three of them?

The natural thing to compute is how long three people take: four people times 6 hours is 24 person-hours, divided by 3 is 8 hours. Eight is almost certainly one of the choices. And it is wrong, because the question said how much longer, which is 8 minus 6, or 2 hours.

Nothing about that question is hard. The arithmetic is one multiplication and one division. The failure is entirely in the reading, and the test writer knew it, which is why 8 hours is sitting there waiting.

Phrases that signal the answer is a difference or a remainder rather than a total:

Underline the question's verb and its unit before you compute anything.

Deciding what each number is for

A word problem hands you numbers in three categories.

Kept. Used directly in the arithmetic.

Converted. Used, but not in the form given. A question that gives you a monthly salary and asks about a week needs a conversion first, and the raw monthly figure will be among the choices for anyone who forgets.

Ignored. Real ASVAB questions do include numbers that go nowhere. A question about the cost of fuel for a trip may tell you the vehicle has four passengers. If passengers are not in the question, the 4 is scenery.

Test writers put unused numbers in for a reason: a reader who believes every number must be used will find a way to use them, and that way will be wrong. Give yourself permission to leave a number on the page.

Translating the words

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Word problems are written in a small, stable vocabulary. These map one to one.

Two of those need care.

"Of" means multiply, almost always, and especially with fractions and percent. Three quarters of 48 is 0.75 times 48.

"Per" cuts both ways. "The truck uses 3 gallons per hour" going into a question about 8 hours is multiplication. "She drove 240 miles on 8 gallons, what is her mileage per gallon" is division. The word tells you a rate is involved; it does not tell you the direction. The unit you are solving for does.

"Less than" and "fewer than" reverse the order. "Six less than a number" is n minus 6, not 6 minus n. This is the most common translation error in algebra-flavored word problems, and it is worth over-learning, because the reversed version is usually an answer choice.

Work one in under a minute

A recruiter drives 45 miles to a high school, then 28 miles to a second school, then returns directly to the office, which is 60 miles from the second school. If the government rate is 67 cents per mile, what is the total reimbursement?

Last sentence first: total reimbursement, in dollars.

Numbers: 45, 28 and 60 are miles and all three are kept - the trip is all three legs. 67 cents is a rate and needs to be 0.67 dollars.

Total miles: 45 plus 28 plus 60 is 133.

Reimbursement: 133 times 0.67. Break it up rather than stacking it: 133 times 0.67 is 133 times 0.5 plus 133 times 0.17, which is 66.50 plus 22.61, or $89.11.

Sanity check: 133 miles at roughly two thirds of a dollar should land near $90. It does.

What you can skip

Across all 1,179 Arithmetic Reasoning questions in our bank, negative numbers, exponents, scientific notation, temperature conversions and 24-hour time never appear. Every question is a situation to be turned into ordinary arithmetic. Across the 146 questions on this topic:

• Coin puzzles come up once. Consecutive-number and age questions do appear (4 and 8), and the translate-then-solve method in this lesson handles them.

Where people lose points

Answering the intermediate value. Covered above, and it is the big one. The intermediate value is always an answer choice.

Missing a unit change. Minutes given, hours asked. Feet given, yards asked. Cents given, dollars asked. The unconverted number is always an answer choice too, and it is the most convincing wrong answer on the test because your arithmetic was correct.

Using a number because it was there. See above on scenery.

Reversing a subtraction or a division. "How many times heavier is A than B" is A divided by B. Getting it backward produces a reciprocal, and the reciprocal will be among the choices.

Rounding partway through. Round at the end, once, to whatever precision the choices use. Rounding in the middle of a multi-step problem can move your answer into the next choice's territory.

A checklist you can actually run

Four steps, roughly twenty seconds of the three and a half minutes:

1. Read the last sentence. Name the unit you are solving for.
2. Read the whole problem. Mark each number as kept, converted, or ignored.
3. Write the setup before you compute anything.
4. Compute, then re-read the question one more time and confirm your answer answers it.

Step 4 is the one people skip and the one that pays.

Where this leads

Every other lesson in this subtest assumes you can get from the paragraph to the setup. This is the one that makes the rest of them work.