ASVAB Test Blog

Feb 18th, 2023

ASVAB Arithmetic Reasoning Practice Questions!

asvab arithmetic reasoning practice questions

ASVAB Arithmetic Reasoning Practice Questions

Many candidates struggle with ASVAB arithmetic reasoning practice questions. What makes this subtest different from Math Knowledge, is that AR is about word problems involving numbers.

This contrasts with Math Knowledge – which is more abstract and concerning topics such as algebra and trigonometry.

Below, we have put together a diverse range of five ASVAB test questions.

Before you read the answer explanations, take out a pen and paper and try to identify the answers yourself. This is a diagnostic test to ensure that we can identify any errors in your line of thinking. If you simply read the explanations, you will never know if you could answer these questions without assistance.

Note: all five ASVAB test practice questions below are reflective of the style and standard of questions you can expect to encounter on the day of your exam.

Arithmetic Reasoning Sample Question 1

Identify the next number in the following sequence: 24, 12, 36, 18, ___

Sequence questions are routinely asked on the ASVAB Arithmetic Reasoning test. You will be presented with a series of numbers and asked to work out what the final number should be.

To correctly answer these questions, candidates must identify a pattern. There are different kinds of pattern but because they involve arithmetic – only addition, multiplication, division, and subtraction – will be involved. Invariably, more than one operation will be involved – which is exactly the case with this question.

In this question, the correct pattern is half, then triple.

Notice that 12 is half of 24, and triple 12 is 36. Similarly, 18 is half of 36, and so triple 18 must be 54. Therefore, the correct answer is 54. The next two numbers in this sequence would be 27 and 81.

Arithmetic Reasoning Sample Question 2

One in seven people report having some kind of allergy. If Richmond Town has a population of 1,890 people, approximately how many people have an allergy?

Many ASVAB arithmetic reasoning practice questions take this format, where you are presented with basic statistics and asked to complete simple arithmetic. What matters here is that you take the time to accurately understand what the question is asking. Second, you must take the time needed to work through the problem in a step-by-step manner. Many ASVAB candidates fall at simple hurdles – rushing through simple problems only to end up at the wrong answer.

In this question, we are told that one in seven people have some form of an allergy. This means that six out of seven people do not. The population of Richmond Town is 1,890 and, by dividing by 7, we can learn how many citizens of the town are likely to have an allergy. Therefore, 270 people have an allergy. Be careful about manually working these numbers out. With a calculator it is easy, but when done manually, you need to take extra time.

Again, it is about following simple methods and ensuring you arrive at the correct conclusion.  

Arithmetic Reasoning Sample Question 3

A vehicle worth $8,000 depreciates 15% each year for 2-years. After two years have elapsed, how much is the vehicle worth?

Depreciation questions are common on the AR subtest, too.

Depreciation is the term used to describe how much value an asset loses over time. In the case of vehicles, they depreciate quite fast. As soon as a new vehicle has been bought, it has already depreciated.

In this question, there is one major factor to consider:

  • That you must work out the value of 15% on two different occasions.

15% is simple to work out. Start with 10% – and 10% of $8,000 is $800. Therefore, 5% is half of this, $400 – so 15% is $1,200.

Many candidates make the mistake of doubling $1,200 (to make $2,400) and then subtracting this value from the original price. This means they arrive at a final value of $5,600. But this is wrong.

That is because after one year has elapsed, the vehicle has lost only $1,200 in value – meaning it is now worth $6,800 after the first years’ depreciation.

Now, we must take another 15% from $6,800 to work out the second-year loss of value.

15% of $6,800 = $1,020

Now, we subtract $1,020 from $6,800 to give us $5,780. And this is how much the vehicle is worth after depreciating 15% each year for two years.

Arithmetic Reasoning Sample Question 4

If 45 gallons of water pass through a pipe in 9 seconds, how many gallons of water pass through the same pipe in 4 seconds?

Again, this is one of the most common ASVAB arithmetic reasoning practice questions – where you are presented with a data set and asked to work out how these figures can be manipulated to find a target answer.

In this question, we are told that 45 gallons of water pass through a pipe in 9 seconds. Therefore, to work out how many gallons of water pass through in 4 seconds, we need to know how many gallons pass through the pipe in 1 second.

45 gallons of water / 9 seconds = 5 gallons per second

If 5 gallons pass through the pipe in 1 second, then 20 gallons must pass through the pipe in 4 seconds.

This kind of problem often features time – hours, minutes, and seconds; and metrics, such as gallons or weight. However, the underlying principle of answering the problem remains the same. Often, it is easier to work out 1 second or 1 hour or 1 of anything, before working upward to higher values – as we have done in this problem.

Arithmetic Reasoning Sample Question 5

36,000 candidates take the ASVAB exam. 25 percent of these candidates did not make it through to selection; and only one-third of those who were selected made it through to join the US air force. How many candidates joined the US air force?

These kinds of arithmetic reasoning questions are common. You are presented with a variety of statistical facts that describe an event. You are then asked to crunch those numbers to find a specific value. In this case, to identify how many candidates from the 36,000 applicants were accepted into the US Air Force.

First, we need to clean things up. 25% of applicants were not selected. We must first remove these people from the 36,000. One-quarter (25%) of 36,000 = 9,000. When we subtract these 9,000 failed applicants, we learn that 27,000 people made it through the ASVAB exam to be selected for one of the major branches of the military.

The question also states that one-third of those who passed and were accepted made it through to join the Air Force. One-third (33%) of 27,000 is 9,000.

Therefore, 9,000 applicants made it through to join the US Air Force.

Take Home Message

The more ASVAB arithmetic reasoning practice questions you take, the greater ability you develop to work problems out.

In the end, that’s what much of the ASVAB test is about: identifying candidates with a high aptitude for problem solving and logical reasoning. Much of the AR subtest is about having a structured, step-by-step approach to each question. It’s also about avoiding the temptation to rush, however “simple” a question may seem at first sight.

Finally, it’s about learning from mistakes. You may have gotten some of these ASVAB test questions wrong. That is a good thing. It means you have an opportunity to ensure the same mistakes do not repeat in the future.

With enough time, practice, and patience, there is no reason why you cannot ace the arithmetic reasoning subtest on the day of your ASVAB exam.

Check back to our blog here at ASVAB Test Practice soon for more exclusive content and features to help you dominate the exam and make it through to boot camp!



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