The Arithmetic Reasoning test consists of arithmetic word problems.
30 questions in 36 minutes
Here are the types of concepts and subjects tested:
The AR part of the AFCT tests your speed and accuracy in performing arithmetic calculations. There are three obstacles people typically encounter when studying for this test:
not quickly recognizing what the question is asking (i.e., not recognizing the type of problem they're looking at),
not being able to do the calculations quickly, and
not really knowing how to study.
Recognizing the type of problem – The problems you'll face on this test fall into three general categories: ratio, percentage, and speed-time-distance.
Ratio problems typically provide you with three facts and require you to figure out the missing fourth fact. Example: A grocery store is selling bananas at 3 pounds for $1. How much would 4 pounds of bananas cost?
On the AR test you're likely to encounter percentage problems of three kinds: straight percentages, tax rates, and discounts.
Example: straight percentage – Forty percent (40%) of the men in the room are bald. There are 38 men in the room. How many are bald?
Example: straight percentage – Sharonda went to dinner with her friends. The bill came to $43.95. If the group decided to leave a 15% tip, how much money should they leave for the tip?
Example: tax rates – Bob is buying a new sound system for $295. The tax rate is 6%. How much does he have to pay?
Example: discounts – Twenty-five percent (25%) of the people at the lecture got bored and left early. If there were 135 people in the lecture when it began, how many were left when it ended?
Speed-time-distance problems are variations of ratio problems. They typically provide you with two factors and require you to figure out the missing third factor. Example: Jim drives for 1 hour at 35mph, 2.5 hours at 55mph, and 35mph for another half hour. How far does he travel altogether?
Once you know what the various types of
problems you're likely to encounter look like, you can practice how to solve
each type. Your goal is to be able to instantly recognize the type of
problem you're being asked to solve, pull out of your memory the way all of
that type of problem are solved, and then actually solve it.
Calculations – All the questions you'll face in the AR test can be solved using the four basic arithmetic operations: addition, subtraction, multiplication, and/or division. You may think this is no big deal, that your problem is not with the calculations but with figuring out what kind of problem you're being asked to solve.
Consider this, however: the test consists of 30 questions; you have 36 minutes to answer them all – that's an average of 1 minutes 12 seconds per question. If you take a minute to figure out what kind of problem you're being asked to solve, can you do the calculations in 12 seconds? The second you put your pencil to the paper, you're taking time you don't need to take. Your main goal, in improving your ability to perform these calculations, should be to do as much of the calculation in your head as possible.
Flash cards are a great way to improve your speed at mental calculation. There are others. Whatever works for you should be what you use.
Within this part of the ASVAB/AFCT, you will be expected to be able to convert simple fractions and decimal numbers into percentages and vice versa.
Example: 1/5 = 20%
Example: 0.63 = 63%
Example: 60% = 3/5
Example: 16% = 0.16
Example: 0.25 = 25% = 1/4
Studying – As with everything else, the key to studying is practice. And practice requires repetition. Going over the same material multiple times is boring. But you can ask friends to take existing practice problems, change things around a bit, and then give them to you to work on. Photocopy sets of practice problems and cut them out, then arrange them by problem type: all the speed-time-distance problems together, all percentage problems together, etc. Then within each group, try to spot commonalities and see if you can sort those in each group into problems that are even more alike than just being “percentage problems” or “ratio problems. Being able to recognize patterns is crucial to doing well on the AR test. Remember: this is a timed test – the more practice problems you do, the quicker you’ll be able to do them when you get one that’s not identical but similar to one you’ve seen in your practice.