ASVAB — All Questions

If 3x + 7 = 22, what is the value of x?

• a.5✓
• b.3
• c.7
• d.9

Subtracting 7 from both sides gives 3x equals 15. Dividing both sides by 3 gives x equals 5. You can check by substituting 5 back into the equation.

What is the value of 4 squared plus 3 cubed?

• a.43✓
• b.25
• c.49
• d.37

Four squared is 16 and three cubed is 27. Adding 16 and 27 gives 43. Exponents are evaluated before addition.

The area of a triangle with base 10 and height 6 is:

• a.30✓
• b.60
• c.45
• d.16

The area of a triangle equals one half times base times height. That is 0.5 times 10 times 6, which equals 30 square units. Forgetting the one-half factor gives the incorrect value 60.

What is the value of x if x/4 = 9?

• a.45
• b.18
• c.36✓
• d.13

To isolate x, multiply both sides of the equation by 4. That gives x equals 9 times 4, or 36. Dividing 36 by 4 returns 9, which confirms the answer.

Simplify: 2(3 + 4) - 5.

• a.12
• b.7
• c.9✓
• d.3

Following order of operations, first add inside the parentheses to get 7. Multiply by 2 to get 14, then subtract 5 to reach 9.

A circle has a radius of 5. What is its circumference? (Use pi is about 3.14.)

• a.78.5
• b.15.7
• c.31.4✓
• d.25.0

Circumference equals 2 times pi times the radius. That is 2 times 3.14 times 5, which equals 31.4. The value 78.5 is the area, not the circumference.

What is the value of the expression 5! (5 factorial)?

• a.720
• b.120✓
• c.60
• d.25

A factorial multiplies all whole numbers from the number down to 1. So 5 factorial is 5 times 4 times 3 times 2 times 1, which equals 120.

Solve for y: 2y - 6 = 10.

• a.8✓
• b.2
• c.16
• d.5

Adding 6 to both sides gives 2y equals 16. Dividing both sides by 2 gives y equals 8. Substituting 8 back confirms the solution.

What is the square root of 144?

• a.12✓
• b.72
• c.11
• d.14

The square root of a number is the value that, multiplied by itself, gives that number. Since 12 times 12 equals 144, the square root of 144 is 12.

The sum of the interior angles of a triangle is:

• a.90 degrees
• b.180 degrees✓
• c.360 degrees
• d.270 degrees

The interior angles of any triangle always add up to 180 degrees. This is a fundamental rule of Euclidean geometry. A quadrilateral, by contrast, totals 360 degrees.

If a = 3 and b = -2, what is the value of a squared minus b?

• a.-11
• b.5
• c.11✓
• d.7

First, a squared is 3 times 3, which equals 9. Subtracting b, which is negative 2, means adding 2, giving 9 plus 2, or 11.

What is 3/4 written as a decimal?

• a.1.33
• b.0.75✓
• c.0.43
• d.0.34

Dividing the numerator 3 by the denominator 4 gives 0.75. Fractions are converted to decimals by dividing the top number by the bottom number.

A rectangle has a length of 8 and a perimeter of 26. What is its width?

• a.4
• b.5✓
• c.9
• d.6

The perimeter equals twice the length plus twice the width. So 26 minus 2 times 8, which is 16, leaves 10 for the two widths. Dividing 10 by 2 gives a width of 5.

Simplify the expression 3x + 2x - x.

• a.5x
• b.2x
• c.6x
• d.4x✓

Combining like terms, 3x plus 2x equals 5x, and subtracting x leaves 4x. Only the coefficients are added and subtracted since all terms share the variable x.

What is the value of 6 divided by 0.5?

• a.3
• b.6
• c.0.083
• d.12✓

Dividing by 0.5 is the same as multiplying by 2. So 6 divided by 0.5 equals 12. Dividing by a number less than 1 produces a result larger than the original.

A cube has edges of length 3. What is its volume?

• a.27✓
• b.18
• c.9
• d.81

The volume of a cube equals the edge length raised to the third power. Three cubed is 3 times 3 times 3, which equals 27 cubic units.

Solve for x: 3x - 7 = 20

• a.9✓
• b.7
• c.11
• d.13

Add 7 to both sides to get 3x = 27, then divide by 3 to get x = 9. Substituting back, 3(9) - 7 = 20.

Solve for x: 5(x + 2) = 45

• a.9
• b.11
• c.7✓
• d.5

Divide both sides by 5 to get x + 2 = 9, so x = 7. Checking, 5(7 + 2) = 5(9) = 45.

What is the value of 4 cubed minus 2 to the fourth power?

• a.56
• b.32
• c.48✓
• d.40

Four cubed is 64 and 2 to the fourth is 16, so 64 - 16 = 48.

Simplify: (x^5)(x^3)

• a.x^15
• b.x^2
• c.2x^8
• d.x^8✓

Multiplying powers of the same base adds the exponents, so 5 + 3 = 8 and the product is x^8. Testing with x = 2 gives 32 x 8 = 256, which is 2^8.

What is the area of a triangle with a base of 14 inches and a height of 9 inches?

• a.126 square inches
• b.46 square inches
• c.63 square inches✓
• d.105 square inches

The area of a triangle is one-half base times height: 0.5 x 14 x 9 = 63 square inches.

Using 22/7 for pi, what is the circumference of a circle whose diameter is 14 inches?

• a.154 inches
• b.22 inches
• c.44 inches✓
• d.88 inches

Circumference equals pi times the diameter: (22/7) x 14 = 44 inches. The value 154 would be the area, not the circumference.

Solve for y: 2y/3 = 12

• a.24
• b.12
• c.8
• d.18✓

Multiply both sides by 3 to get 2y = 36, then divide by 2 to get y = 18.

Which of the following is the factored form of x^2 - 9?

• a.(x + 3)(x - 3)✓
• b.(x - 3)(x - 3)
• c.(x + 3)(x + 3)
• d.(x + 9)(x - 1)

A difference of two squares factors as (x + 3)(x - 3). Testing at x = 5, the original is 16 and the factored form is 8 x 2 = 16.

What is 25 percent of three-fifths of 200?

• a.40
• b.50
• c.24
• d.30✓

Three-fifths of 200 is 120, and 25 percent of 120 is 30.

If a = 3 and b = -2, what is the value of a^2 - 2ab?

• a.-3
• b.9
• c.33
• d.21✓

a^2 is 9, and 2ab is 2(3)(-2) = -12. Subtracting a negative adds, so 9 + 12 = 21.

What is the slope of the line passing through the points (-1, 2) and (3, 14)?

• a.4
• b.2
• c.3✓
• d.6

Slope is the change in y over the change in x: (14 - 2) / (3 - (-1)) = 12 / 4 = 3.

What is the volume of a rectangular box measuring 5 inches by 4 inches by 3 inches?

• a.60 cubic inches✓
• b.47 cubic inches
• c.120 cubic inches
• d.12 cubic inches

Volume is length times width times height: 5 x 4 x 3 = 60 cubic inches.

Solve the inequality: 4x + 3 < 19

• a.x > 4
• b.x < 5.5
• c.x > 5.5
• d.x < 4✓

Subtract 3 to get 4x < 16, then divide by 4 to get x < 4. Dividing by a positive number leaves the inequality sign unchanged.

What is the square root of 144 plus the square root of 25?

• a.19
• b.169
• c.17✓
• d.13

The square root of 144 is 12 and the square root of 25 is 5, so the sum is 17.

A square has an area of 81 square feet. What is its perimeter?

• a.18 feet
• b.27 feet
• c.36 feet✓
• d.40 feet

The side of the square is the square root of 81, or 9 feet. The perimeter is 4 x 9 = 36 feet.

Simplify: 3(2x - 4) + 5x

• a.11x - 4
• b.11x - 12✓
• c.6x - 12
• d.11x + 12

Distributing gives 6x - 12, and adding 5x gives 11x - 12. Testing at x = 7, the original is 65 and 11(7) - 12 is also 65.

If 3^x = 81, what is the value of x?

• a.3
• b.4✓
• c.27
• d.9

Because 3 x 3 x 3 x 3 = 81, x is 4.

What is the sum of the interior angles of a pentagon?

• a.360 degrees
• b.720 degrees
• c.450 degrees
• d.540 degrees✓

The interior angles of an n-sided polygon sum to (n - 2) x 180 degrees, so a pentagon gives 3 x 180 = 540 degrees.

Which of the following numbers is prime?

• a.57
• b.61✓
• c.51
• d.69

The other three all divide by 3: 51 = 3 x 17, 57 = 3 x 19, and 69 = 3 x 23. Only 61 has no factors besides 1 and itself.

What is 3/8 written as a decimal?

• a.0.375✓
• b.0.625
• c.0.325
• d.0.380

Dividing 3 by 8 gives 0.375. The value 0.625 is 5/8, the complement of this fraction.

If x + y = 10 and x - y = 4, what is the value of y?

• a.7
• b.3✓
• c.6
• d.4

Subtracting the second equation from the first gives 2y = 6, so y = 3 and x = 7.

A right triangle has legs measuring 9 inches and 12 inches. How long is the hypotenuse?

• a.21 inches
• b.18 inches
• c.15 inches✓
• d.13 inches

By the Pythagorean theorem, 9^2 + 12^2 = 81 + 144 = 225, and the square root of 225 is 15.

Reduce the ratio 18:24 to lowest terms.

• a.3:4✓
• b.6:8
• c.2:3
• d.4:5

Both terms divide by 6, giving 3:4. The ratio 6:8 has the same value but is not in lowest terms.

What is the value of 5 factorial?

• a.20
• b.25
• c.720
• d.120✓

Five factorial is 5 x 4 x 3 x 2 x 1 = 120. The value 720 is 6 factorial.

Which values of x satisfy x^2 - 5x + 6 = 0?

• a.x = 2 or x = 3✓
• b.x = 5 or x = 6
• c.x = -2 or x = -3
• d.x = 1 or x = 6

The expression factors as (x - 2)(x - 3), so the roots are 2 and 3. Both must be positive because their product is +6 and their sum is +5.

Using 3.14 for pi, what is the area of a circle with a diameter of 10 inches?

• a.314.0 square inches
• b.62.8 square inches
• c.78.5 square inches✓
• d.31.4 square inches

The radius is half the diameter, or 5 inches. Area is pi times the radius squared: 3.14 x 25 = 78.5 square inches.

What is 8 percent of 350?

• a.28✓
• b.32
• c.42
• d.24

One percent of 350 is 3.5, so 8 percent is 8 x 3.5 = 28.

Simplify: (2x^3y^2)(4xy^4)

• a.8x^3y^8
• b.6x^4y^6
• c.2x^4y^6
• d.8x^4y^6✓

Multiply the coefficients, 2 x 4 = 8, and add the exponents of each variable: x^(3+1) and y^(2+4). Testing at x = 2 and y = 3 gives 93,312 both ways.

A rectangle has a perimeter of 46 inches and a length of 14 inches. What is its width?

• a.9 inches✓
• b.16 inches
• c.18 inches
• d.32 inches

Half the perimeter is one length plus one width, or 23 inches. Subtracting the 14-inch length leaves a width of 9 inches.

What is the median of the numbers 3, 11, 7, 2, and 9?

• a.6
• b.8
• c.9
• d.7✓

Put the numbers in order as 2, 3, 7, 9, 11 and take the middle value, which is 7. The mean of the same list is 6.4, not the median.

Solve for x: x/4 + 3 = 11

• a.32✓
• b.56
• c.24
• d.8

Subtract 3 to get x/4 = 8, then multiply by 4 to get x = 32.

Which of these fractions has the greatest value?

• a.7/12
• b.2/3✓
• c.3/5
• d.5/8

Written over a common denominator of 120 they are 75/120, 80/120, 70/120, and 72/120, so 2/3 is the largest.

What is the distance between the points (1, 2) and (7, 10)?

• a.14 units
• b.100 units
• c.10 units✓
• d.8 units

The horizontal change is 6 and the vertical change is 8, so the distance is the square root of 36 + 64 = 100, which is 10.

What is the square root of 50 in simplest radical form?

• a.2 times the square root of 5
• b.25 times the square root of 2
• c.5 times the square root of 2✓
• d.10 times the square root of 5

Since 50 = 25 x 2 and 25 is a perfect square, the root becomes 5 times the square root of 2, or about 7.07.

A number increased by 25 percent equals 90. What is the number?

• a.65
• b.70
• c.75
• d.72✓

The result is 125 percent of the number, so the number is 90 / 1.25 = 72. Checking, 25 percent of 72 is 18, and 72 + 18 = 90.

What is the value of (3^2)^3?

• a.27
• b.729✓
• c.243
• d.81

Raising a power to a power multiplies the exponents, giving 3^6 = 729.

In a right triangle, one acute angle measures 35 degrees. What does the other acute angle measure?

• a.55 degrees✓
• b.65 degrees
• c.45 degrees
• d.145 degrees

The two acute angles of a right triangle add to 90 degrees, so the second is 90 - 35 = 55 degrees.

What is the value of 8 + 2 x (6 - 2)^2 / 4?

• a.16✓
• b.12
• c.40
• d.24

Work inside the parentheses first: 6 - 2 = 4, and 4 squared is 16. Then 2 x 16 = 32, 32 / 4 = 8, and 8 + 8 = 16.

What is the reciprocal of 2/7?

• a.7/2✓
• b.1/7
• c.2/7
• d.-2/7

A reciprocal flips the numerator and denominator, so 2/7 becomes 7/2. Their product is 1.

Two triangles are similar. The smaller has sides of 3, 4, and 5 inches, and the larger has a shortest side of 12 inches. How long is the larger triangle's longest side?

• a.20 inches✓
• b.25 inches
• c.15 inches
• d.16 inches

The scale factor is 12 / 3 = 4, so every side is multiplied by 4. The longest side becomes 5 x 4 = 20 inches.

Solve for x: 2(x - 3) = x + 5

• a.16
• b.8
• c.14
• d.11✓

Distributing gives 2x - 6 = x + 5. Subtracting x from both sides and adding 6 gives x = 11.

Using 3.14 for pi, what is the volume of a cylinder with a radius of 3 inches and a height of 10 inches?

• a.282.6 cubic inches✓
• b.314.0 cubic inches
• c.188.4 cubic inches
• d.94.2 cubic inches

Volume equals pi times radius squared times height: 3.14 x 9 x 10 = 282.6 cubic inches.

What is 5/4 expressed as a percent?

• a.125%✓
• b.145%
• c.45%
• d.80%

Dividing 5 by 4 gives 1.25, and moving the decimal two places right gives 125 percent. Any fraction greater than 1 exceeds 100 percent.

If f(x) = 2x^2 - 3x, what is f(4)?

• a.20✓
• b.26
• c.12
• d.44

Substituting 4 gives 2(16) - 3(4) = 32 - 12 = 20.

The sum of three consecutive even integers is 78. What is the largest of the three?

• a.24
• b.28✓
• c.26
• d.30

Calling the smallest x gives 3x + 6 = 78, so x = 24 and the integers are 24, 26, and 28. Their sum checks out at 78.

What is 3/4 divided by 2/3?

• a.8/9
• b.1/2
• c.3/2
• d.9/8✓

Dividing by a fraction means multiplying by its reciprocal: 3/4 x 3/2 = 9/8.

Two angles are supplementary, and one is three times the size of the other. How large is the smaller angle?

• a.45 degrees✓
• b.60 degrees
• c.135 degrees
• d.30 degrees

Supplementary angles add to 180 degrees. Splitting 180 into 4 equal parts gives 45 for the smaller angle and 135 for the larger.

For x not equal to 3, simplify (x^2 - x - 6) / (x - 3).

• a.x + 3
• b.x - 6
• c.x + 2✓
• d.x - 2

The numerator factors as (x - 3)(x + 2), and the (x - 3) terms cancel. Testing at x = 10 gives 84 / 7 = 12, which matches 10 + 2.

What is the least common multiple of 12 and 18?

• a.216
• b.54
• c.36✓
• d.6

Multiples of 18 are 18, 36, 54, and 36 is the first one that 12 also divides. The value 6 is the greatest common factor, not the least common multiple.

A cube has a volume of 216 cubic inches. How long is one edge?

• a.36 inches
• b.6 inches✓
• c.12 inches
• d.8 inches

The edge is the cube root of the volume, and 6 x 6 x 6 = 216 inches.