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Arithmetic Reasoning ASVAB Test 2025 - 2026
With Complete Solutions
What is 12/60 converted to a percentage?
a. 0.
b. 20%
c. 25%
d. 12%
e. 1.2% - ✔✔The fraction 12/60 can be reduced to 1/5 , in lowest terms. First, it must be converted to a decimal. Dividing 1 by 5 results in 0.2. Then, to convert to a percentage, move the decimal point two units to the right and add the percentage symbol. The result is 20%.
Which of the following is the correct decimal form of the fraction 14/33 rounded to the nearest hundredth place?
a. 0.
b. 0.
c. 0.
d. 0.
e. 0.42 - ✔✔E: If a calculator is used, divide 33 into 14 and keep two decimal places. If a calculator is not used, multiply both the numerator and denominator times 3. This results in the fraction 42/99, and hence an approximate decimal of 0.42.
Which of the following represents the correct sum of 14/15 and 2/5? - ✔✔B: Common denominators must be used. The LCD is 15, and 2/5 = 6/15 Therefore, 14/15 + 6/15 = 20/15 ,
and in lowest terms, the answer is A common factor of 5 was divided out of both the numerator and denominator.
What is the product of and 5/14 and 7/20? - ✔✔A: A product is found by multiplication. Multiplying two fractions together is easier when common factors are cancelled first to avoid working with larger numbers.
5/14 x 7/20 = 5/2x7 x 7/5x
1/2 x 1/4 = 1/
What is the result of dividing 24 by 8/5? - ✔✔D: Division is completed by multiplying by the reciprocal. Therefore:
24 divided 8/5 = 24/1 x 5/
(3x8)/1 x 5/8 = 15/1 = 15
Subtract 5/14 from 5/24 Which of the following is the correct result? - ✔✔C: Common denominators must be used. The LCD is 168, so each fraction must be converted to have 168 as the denominator.
5/24 - 5/14 = 5/24 x 7/7-5/14x12/
b. 20
c. 21
d. 25
e. 18 - ✔✔C: Gina answered 60% of 35 questions correctly; 60% can be expressed as the decimal 0.60.
Therefore, she answered 0.60 × 35 = 21 questions correctly.
Paul took a written driving test, and he got 12 of the questions correct. If he answered 75% of the total questions correctly, how many problems were on the test?
a. 25
b. 15
c. 20
d. 18
e. 16 - ✔✔E: The unknown quantity is the number of total questions on the test. Let be equal to this unknown quantity. Therefore, 0.75x = 12 Divide both sides by 0.75 to obtain x = 16.
If a car is purchased for $15,395 with a 7.25% sales tax, what is the total price?
a. $15,395.
b. $16,511.
c. $16,411.
d. $15,
e. $16,113.10 - ✔✔B: If sales tax is 7.25%, the price of the car must be added by the this additional tax.
To start,
- Convert 7.25% to a decimal by dividing by 100. (Move left 2 spots)
- 1 must be added to 0.0725 to calculator the total price this is the equation. This is for all cases.
Purchased price × (1+ sales tax decimal form)
15395 x 1.0725 (move decimal 4 times to the right to multiply)
They are asking for an exact number so we have to multiply the long way.
x
165,111, 375 ( Now go back 4 times)
16511.1375 ( Round to the hundredths)
d. $5,
e. $1,200 - ✔✔D: There are 52 weeks in a year, and if the family spends $105 each week, that amount is close to $100. A good approximation is $100 a week for 50 weeks, which is found through the product 50x 100= $5,000.
Bindee is having a barbeque on Sunday and needs 12 packets of ketchup for every 5 guests. If 60 guests are coming, how many packets of ketchup should she buy? a. 100
b. 12
c. 144
d. 60
e. 300 - ✔✔C: This problem involves ratios and percentages. If 12 packets are needed for every 5 people, this statement is equivalent to the ratio The unknown amount x is the number of ketchup packets needed for 60 people. The proportion 12/5 = x/60 must be solved. Cross- multiply to obtain 12 x 60 =5x Therefore, 720=5x. Divide each side by 5 to obtain x = 144 packets.
A grocery store sold 48 bags of apples in one day, and 9 of the bags contained Granny Smith apples. The rest contained Red Delicious apples. What is the ratio of bags of Granny Smith to bags of Red Delicious that were sold?
a. 48:
b. 39:
c. 9:
d. 9:
e. 39:48 - ✔✔D: There were 48 total bags of apples sold. If 9 bags were Granny Smith and the rest were Red Delicious, then 48 - 9 = 39 bags were Red Delicious. Therefore, the ratio of Granny Smith to Red Delicious is 9:39.
If Oscar's bank account totaled $4,000 in March and $4,900 in June, what was the rate of change in his bank account total over those three months?
a. $900 a month
b. $300 a month
c. $4,900 a month
d. $100 a month
e. $4,000 a month - ✔✔B: The average rate of change is found by calculating the difference in dollars over the elapsed time. Therefore, the rate of change is equal to $4,900-$4,000÷ 3 months, which is equal to $900÷3 or $300 a month.
How is a transposition of a matrix performed?
a. Multiply each number by negative 1 rows and columns
b. Switch the rows and columns
c. Reverse the order of each row
d. Find the inverse of each number
e. Divide the first number in each row by the last number in the last column - ✔✔B: because the
definition of transposing a matrix says that the rows and columns should be switched. For example, the matrix
3 4
2 5
What are the two values that always describe a vector?
a. Magnitude and direction
b. Magnitude and length
c. Length and position
d. Direction and position
e. Magnitude and position - ✔✔A: The vector is described as having both magnitude and direction. The magnitude is the size of the vector and the direction is the path along with which the force is being applied. The second answer choice has magnitude and length, which are essentially the same. The third, fourth, and fifth answer choices include length and position, but position is also not part of the description of a vector.
What is the resultant matrix when addition is performed? - ✔✔C: The correct answer is Choice C because matrices are added by adding the corresponding numbers in the two given matrices. For matrices to be added, they must have the same number of rows and columns. These two matrices have two rows and two columns. The first row, first column numbers are 1 and 3, and adding them together yields a total of 4. The second row, first column has numbers 4 and -2, which yields a sum of 2. The first row, second column has -5 and 2, which sum to -3. The second row, second column have 2 and 1, which yield a sum of 3. The resulting matrix after addition is:
4 -
2 3
Which set of matrices represents the following system of equations? - ✔✔D: The correct matrix to describe the given system of equations is the last matrix (Choice D) because it has values that correspond to the coefficients in the right order. The top row corresponds to the coefficient in the first equation, the second row corresponds to the coefficients in the second equation, and the
third row corresponds to the coefficients in the third equation. The second matrix (Choice B) is filled with the three variables in the system. One thing to also look for is the sign on the numbers, to make sure the signs are correct from the equation to the matrix.
Which label describes the relationship between these vectors? - ✔✔D: The picture shows how vectors are added. According to the definition, the vectors must be placed head to tail, then the resulting vector is drawn from the beginning head to the ending tail. Notice that the vector runs from the bottom left to the top right. Adding these vectors in the wrong direction would yield a vector starting at the top right, at the end of vector v, and ending at the bottom left.
What is the name of the indicated part of Vector B? - ✔✔B: The answer is Choice B because the part of the vector that the arrow points to is the tail. The end of a vector with the arrow is called the head. The opposite end, without the arrow, is called the tail.
When two vectors are added, what is the answer called?
a. Ending vector
b. Total vector
c. Summation vector
d. Resolved vector
e. Resultant vector - ✔✔E: When two vectors are added, the resulting vector is called the
resultant. By definition, the vector found from addition of two or more vectors is the resultant. The other choices of ending vector and total vector could refer to one or more of the starting vectors, not the resultant.
If a pound of rice costs $4.20, how much does ¾ pound cost?
60% of which number is equal to 19?
A. 33.
B. 31.
C. 40.
D. 11.
E. 72.41 - ✔✔Answer: B.
60%x = 19 - Solve for x
Divide 60% each side
Without factoring in hourly wages, a restaurant server makes an average of 18% tips on $570 in sales over the course of a 6 hour shift. How much did the server make in tips (total) during said shift?
A. $
B. $131.
C. $31.
D. $102.
E. $10.26 - ✔✔Answer: D.
570 x 18% - Make the percent into decimal and move 2 spaces to make whole
570 x 18 = 10,260 - Move 2 decimal points back
102.60 Which is D.
If the smallest angle in a right triangle is 32 degrees, what are the degree spans of the other two angles?
A. 90 degrees, 58 degrees
B. 90 degrees, 68 degrees
C. 80 degrees, 68 degrees
D. 80 degrees, 58 degrees
E. 90 degrees, 48 degrees - ✔✔Answer: A.
We know one of the sides is 90 since its a right angle.
We are giving info that the smallest angle is 32. There are only 3 sides to a triangle.
Subtract 90 by 32 = Which is 58.
Check: Triangle is 180 total. Add 90+32+58 = 180. Answer A is the right choice.
One lap on a particular outdoor track measures a quarter of a mile around. To run a total of three- and-a-half miles, how many laps must a person complete?
A. 7
B. 9
C. 11
D. 12
E. 14 - ✔✔Answer: E.
1 lap = 1/
We need to run a total of 3.5 miles.
So think how many 1/4's do we need to get to 3.
1/4x = 3.5 - Multiply both sides by 4 to isolate the x
1x = 3.5 x 4 - Move decimal of 3.5 to the right to multiply
35 x 4 = 140 - Move decimal back to the left once
1x = 14.0 = x = 14 which is E.
The basal metabolic rate (BMR) is the rate at which our bodies use calories. The BMR for a man in his twenties is about 1,700 calories per day. If 204 of those calories should come from protein, about what percentage of this man's diet should be protein?
A. 1.2%
B. 8.3%
C. 12%
D. 16%
E. 18% - ✔✔Answer: C.
The problem is solved by dividing 204/1700.
Now 204 is closer to 200, we can think this way as the question states that it is "about what percentage".
200/1700 can be reduced by 100 to get 2/17, Now 17 is closer to 20 so if we do 2/20 we get 10%, 2/17 would be a bit higher so the closest is C. 12%
Jason is six times as old as Kate. In two years, Jason will be twice as old as Kate is then. How old is Jason now?
A. 3 years old
4k=2 - divide 4 to both sides
K= 2/4 or 1/
Sub 1/2 into the initial 6k
6(1/2) = 6/2 or 3 which is answer A
You will have 29 minutes to answer the 25 questions that are on the Arithmetic Reasoning Subtest when you take the AFOQT. What is the maximum amount of time you should spend on any single question (in seconds)?
Note: Assume each question will warrant the same 'maximum time' for the sake of this problem.
A. 55 seconds
B. 69.6 seconds
C. 88.1 seconds
D. 99.3 seconds
E. 119 seconds - ✔✔Answer B.
Convert 29 minutes to seconds.
Divide 1740 seconds by the amount of questions
A hiker walks 40 miles on the first day of a five-day trip. On each day after that. he can walk only half as far as he did the day before. On average, how far does he walk each day?
A. 10 miles
B. 15.5 miles
C. 20 miles
D. 24 miles - ✔✔Answer is B.
It says each day is halved by the previous day so this is the sequence to get the average.
First day is 40
Second day is 20
Third day is 10
4th day is 5
5th day is 2.
Add all 40+20+10+5+2.5 = 77.
