Tips for Tackling Word Problems on the ASVAB

By Rod Powers

ASVAB test-takers often waste a lot of time reading and rereading word problems as if the answer might reveal itself to them by some miracle; however, correctly solving math word problems requires you to perform a series of organized steps:

  • Read the problem completely.
  • Figure out what the question is asking.
  • Dig out the relevant facts.
  • Set up one or more equations to arrive at a solution and then solve the problem.
  • Review your answer.

Reading the entire problem

The first step in solving a word problem is reading the entire problem to discover what it’s all about. Try forming a picture about the problem in your mind or — better yet — draw a sketch of the problem on your scratch paper. Ask yourself whether you’ve ever seen a problem like this before. If so, what’s similar about it, and what did you do to solve it in the past?

Figuring out what the question is asking

The second and most important step in solving a word problem is to determine exactly what the question is asking. Sometimes the question is asked directly. At other times, identifying the actual question may be a little more difficult. Suppose you’re asked the following question:

  1. What’s the volume of a cardboard box measuring 12 inches long by 14 inches wide by 10 inches tall?
    • A. 52 cubic inches
    • B. 88 cubic inches
    • C. 120 cubic inches
    • D. 1,680 cubic inches

The problem directly asks you to determine the volume of a cardboard box. Recall from your high school algebra and geometry classes that the volume of a rectangular container is length × width × height, or V= lwh. So 12 × 14 × 10 = 1,680. The correct answer is Choice (D).

Now take a look at the next example:

  1. How many cubic inches of sand can a cardboard box measuring 12 inches long by 14 inches wide by 10 inches tall contain?
    • A. 52 cubic inches
    • B. 88 cubic inches
    • C. 120 cubic inches
    • D. 680 cubic inches

This is the same problem, but the question you need to answer isn’t as directly stated. Therefore, you have to use clues embedded in the problem to figure out what the actual question is. Would figuring out the perimeter of the box help you with this question? Nope. Would figuring out the area of one side of the box help you? Nope — you’re not painting the box; you’re filling it. The question wants you to determine the volume of the container.

Clue words can be a big help when trying to figure out which question is being asked. Look for the following clue words:

  • Addition: Sum, total, in all, perimeter, increased by, combined, added
  • Division: Share, distribute, ratio, quotient, average, per, out of, percent
  • Equals: Is, was, are, were, amounts to
  • Multiplication: Product, total, area, cubic, times, multiplied by, of
  • Subtraction: Difference, how much more, exceed, less than, fewer than, decreased

Digging for the facts

After you figure out which question you’re answering, the next step is to figure out which data is necessary to solve the problem and which data is extra. Start by identifying all the information and variables in the problem and listing them on your scratch paper. Make sure you attach units of measurement contained in the problem. After you’ve made a list of the facts, try to eliminate those facts that aren’t relevant to the question. Look at the following example:

To raise money for the school yearbook project, Tom sold 15 candy bars, Becky sold 12 candy bars, Debbie sold 17 candy bars, and Jane sold the most at 50. How many candy bars were sold by the girls?

The list of facts may look something like this:

Tom = 15 bars
Becky = 12 bars
Debbie = 17 bars
Jane = 50 bars
? = total sold by the girls

Because the question is the total number of candy bars sold by the girls, the number of bars sold by Tom isn’t relevant to the problem and can be scratched off the list. Just add the remaining bars from your list. The answer is 79.

Setting up the problem and working your way to the answer

You need to decide how the problem can be solved and then use your math skills to arrive at a solution. For instance, a question may ask the following:

Joan just turned 37. For 12 years, she’s dreamed of traveling to Key West to become a beach bum. To finance this dream, she needs to save a total of $15,000. How much does Joan need to save each year if she wants to become a beach bum by her 40th birthday?

Write down, in mathematical terms, what the question is asking you to determine. Because the question is asking how much money Joan needs to save per year to reach $15,000, you can say y (years Joan has to save) × m (money she needs to save each year) = $15,000. Or to put it more mathematically,

ym = $15,000

You don’t know the value of m (yet) — that’s the unknown you’re asked to find. But you can find out the value of y — the number of years Joan has to save. If she’s 37 and wants to be a beach bum by the time she’s 40, she has 3 years to save. So now the formula looks like this:

3m = 15,000

To isolate the unknown on one side of the equation, you simply divide each side by 3, so 3m ÷ 3 = 15,000 ÷ 3. Therefore, your answer is

m = 5,000

Joan needs to save $5,000 each year for 3 years to reach her goal of $15,000 by the time she’s 40. You may be tempted to include the 12 years Joan has been dreaming of this trip in your formula. This number was put into the problem as a distraction. It has no bearing on solving the problem.

Reviewing your answer

Before marking your answer sheet or punching in that choice on the computer, review your answer to make sure it makes sense. Review by asking yourself the following questions:

  • Does your solution seem probable?
  • Does it answer the question asked?
  • Are you sure?
  • Is your answer expressed using the same units of measurement as used in the problem?