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ASVAB Arithmetic Reasoning | 350 Questions
with complete Solutions | Latest 2023/
What is 12/60 converted to a percentage? a. 0. b. 20% c. 25% d. 12% e. 1.2% - ANSWER>>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 - ANSWER>>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? - ANSWER>>B: Common denominators must be used. The LCD is 15, and 2/5 = 6/ 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? - ANSWER>>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? - ANSWER>>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? - ANSWER>>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/
35/168 - 60/168 = -25/
Which of the following is a correct mathematical statement? - ANSWER>>E: The correct mathematical statement is the one in which the number to the left on the number line is less than the number to the right on the number line. It is written in ANSWER E that , which is the same as a correct statement.
Which of the following is incorrect? - ANSWER>>C: - 1/5 > 4/5 is incorrect. The expression on the left is negative, which means that it is smaller than the expression on the right. As it is written, the inequality states that the expression on the left is greater than the expression on the right, which is not true.
In a neighborhood, 15 out of 80 of the households have children under the age of
- What percentage of the households have children? a. 0.1875%
d. $15, e. $16,113.10 - ANSWER>>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)
7.25/100 = 0.
- 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.
15395 10725 x
165,111, 375 ( Now go back 4 times)
16511.1375 ( Round to the hundredths)
ANSWER comes out as $16,511.14 which is B the ANSWER.
A car manufacturer usually makes 15,412 SUVs, 25,815 station wagons, 50, sedans, 8,123 trucks, and 18,312 hybrids a month. About how many cars are manufactured each month? a. 120, b. 200, c. 300, d. 12, e. 20,000 - ANSWER>>A: Rounding can be used to find the best approximation. All of the values can be rounded to the nearest thousand. 15,412 SUVs can be rounded to 15,000. 25,815 station wagons can be rounded to 26,000. 50, sedans can be rounded to 50,000. 8,123 trucks can be rounded to 8,000. Finally, 18,312 hybrids can be rounded to 18,000. The sum of the rounded values is 117,000, which is closest to 120,000.
Each year, a family goes to the grocery store every week and spends $105. About how much does the family spend annually on groceries? a. $10, b. $50, c. $ d. $5, e. $1,200 - ANSWER>>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 - ANSWER>>C: This problem involves ratios and percentages. If 12 packets are needed for every 5 people, this statement is equivalent to the ratio The
e. Divide the first number in each row by the last number in the last column - ANSWER>>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 1 6 can be transposed into 3 2 1 4 5 6
Notice that the first row, 3 and 4, becomes the first column. The second row, 2 and 5, becomes the second column. This is an example of transposing a matrix.
What is the label given to a problem that multiplies a matrix by a constant? a. Vector multiplication b. Scalar multiplication c. Inverse of a matrix d. Transposition of a matrix e. Product of a matrix - ANSWER>>The correct ANSWER is Choice B because multiplying a matrix by a constant is called scalar multiplication. A scalar is a constant number, which means the only thing it changes about a matrix is its magnitude. For a given matrix, 3 4 6 5 scalar multiplication can be applied by multiplying by 2, which yields the matrix 6 8 12 10
Notice that the dimensions of the matrix did not change, just the magnitude of the numbers.
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 - ANSWER>>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? - ANSWER>>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? - ANSWER>>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.
Of 7,562 college students, 3,451 have taken part in some intramural sport program. What percentage of students have played intramural sports?
A. 56.7% B. 52.1% C. 45.6% D. 50.6% E. 60.4% - ANSWER>>ANSWER: C.
3451/7562 = 0.456 to make percent multiply by 100 (Move decimal twice to the right.
45.6%
60% of which number is equal to 19? A. 33. B. 31. C. 40. D. 11. E. 72.41 - ANSWER>>ANSWER: B.
60%x = 19 - Solve for x
Divide 60% each side
19/.60 = 31.
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. $10.2 6 - ANSWER>>ANSWER: D.
570 x 18% - Make the percent into decimal and move 2 spaces to make whole
.18 → 18
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>>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.
What is the estimated product when 157 and 817 are rounded to the nearest hundred and multiplied?
A. 16, B. 80,
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>>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
B. 6 years old C. 9 years old D. 12 years old E. 15 years old - ANSWER>>ANSWER: A.
"Jason is six times as old as Kate" = 6K
In 2 years = Jason + 2 and K+
Twice as old as Kate = 2 (k+2)
Kate is also 2 years older
So it will be j+2 = 2(k+2)
Substitute 6k for J
6K+2 = 2(k+2)
6k+2=2k+4 - sub 2 to both sides
6k=2k+2 - sub 2k to both sides
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
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.
Now for average divide by how many numbers there are which is 5
77.5/5 = 15.5 which is B.
Mr. Thaler is driving from Los Angeles to San Francisco. If he drives 3 hours in Traffic at an average speed of 32 miles an hour, and then 4.5 hours on the freeway, at an average speed of 72 miles per hours what was his overall average speed on his trip to San Francisco?
A. 45 miles per hour B. 52 miles per hour C. 56 miles per hour D. 60 miles per hour - ANSWER>>ANSWER: C.
We need to first find the total mileage
3 hours = 32 miles/hr We multiply 3 x 32 = 96
4.5 hours = 72 miles/hr We multiply 4.5 x 72 = 324
Add both 324 + 96 = 420
420 - total travel
Now we need to divide by the time
3 hours + 4.5 hours = 7.5 hours
420/7.5 = 56 miles per hour.
If a car is towed 12 miles to the repair shop and the tow charge is $3.50 per mile, how much does the tow cost? (a) $12. (b) $3. (c) $42. (d) $100.00 - ANSWER>>ANSWER C.
1 mile = 3.
We need to know how much 12 miles is so we multiply
3.50 x 12 = $42.
The sum of two numbers is 70. One number is 8 more than the other. What's the smaller number? (a) 31 (b) 33 (c) 35 (d) 36 - ANSWER>>ANSWER: A.
The sum of two numbers
x + x
one number is 8 more than the other
x + x + 8 = 70 - Solve
375 x .12 - move decimal twice to make whole and multiply
375 x 12 = 4500 - move back 2
ANSWER is 45 B.
Carpet stain protector costs $0.65 per square yard to apply. How much will it cost to apply the protectant to a 16-foot by 18-foot carpet?
A. $187. B. $62. C. $20. D. $96.00 - ANSWER>>ANSWER: C.
First we need to find the area of the carpet
- Area = Length x width
16ft x 18ft = 288ft² - its ft² this is important
- Now we must convert the ft into yards 3 ft = 1 yard
Because we are dealing with square feet the 3 ft in 1 yard will be squared as well so it will be 9 ft per yard in this scenario.
288ft ÷ 9 = 32yd²
- Now its $0.65 per yard so now we just need to multiply 32 by 0.
0.65 x 32 - Change .65 to whole
65 x 32 = 2080- move back 2
20.80 is your ANSWER which is C.
A printing plant that produces baseball cards has a monthly overhead of $6,000. It costs 18 cents to print each card, and the cards sell for 30 cents each. How many cards must the printing plant sell each month in order to make a profit?
A. 30, B. 40, C. 50, D. 60,000 - ANSWER>>ANSWER: C.
We need to know how many cards they need to sell to make a profit.
- Cards cost 18 cents to print and they sell for 30 cents. Remember cents means there is a decimal before the whole number.
.30-.18 = .12 -How much they make per card.
- So how many cards (.12) will it take to get to 6,000.
6,000 ÷ .12 -make decimal whole. What you change in the decimal you change in the number being divided.
600,000 ÷ 12 = 50,000 which is C.
Joe received an hourly wage of $8.15. His boss gave him a 7% raise. How much does Joe make per hour now? (a) $0. (b) $8. (c) $8. (d) $13.85 - ANSWER>>ANSWER C.
