Asvab- Mathematics Knowledge

1. 5#4 =

B. 9

A. 5

The correct answer is D. Because 2#3 = 6, the # symbol indicates multiplication. Therefore, 5#4 = 5 × 4 = 20.

C. 16

The # symbol indicates multiplication, so 5#4 = 5 × 4 = 20.

Explanation

The # symbol indicates multiplication, so 5#4 = 5 × 4 = 20.

2. Four-fifths of the seats in a movie theater are filled and two-thirds of the people in the theater are children. What fraction of the total seats are filled with children?

(3/10)

(2/5)

Multiply the fraction of the seats that are filled by the fraction of the people that are children:

(8/15)

To find the fraction of seats filled with children, you multiply the fraction of seats filled (4/5) by the fraction of people that are children (2/3). This results in (4/5) * (2/3) = (8/15). Therefore, the correct answer is (8/15) of the total seats are filled with children.

Explanation

To find the fraction of seats filled with children, you multiply the fraction of seats filled (4/5) by the fraction of people that are children (2/3). This results in (4/5) * (2/3) = (8/15). Therefore, the correct answer is (8/15) of the total seats are filled with children.

3. An isosceles triangle always has

Three unequal sides

No angles measuring 90°

An isosceles triangle is a triangle with two equal sides and two equal angles. It can have one right angle, one obtuse angle, or one angle measuring 45°, but it doesn't always.

Three equal sides

An isosceles triangle specifically has two equal sides and two equal angles, unlike the incorrect options provided which do not align with the definition of an isosceles triangle.

Explanation

An isosceles triangle specifically has two equal sides and two equal angles, unlike the incorrect options provided which do not align with the definition of an isosceles triangle.

4. If k = -2, then k + k(k) =

-2

-4

0

Plug –2 in for k in the given equation: –2 + –2(–2) = –2 + 4 = 2.

To solve the equation, plug -2 in for k: -2 + (-2)(-2) = -2 + 4 = 2

Explanation

To solve the equation, plug -2 in for k: -2 + (-2)(-2) = -2 + 4 = 2

5. If 2x - 7 = 3, then 3x + 1 =

22

Solve the first equation for x: Then plug that value of x into the second equation to find its value: 3(5) + 1 = 15 + 1 = 16.

10

12

To solve the first equation, we add 7 to both sides to get 2x = 10, then divide by 2 to find x = 5. Plugging x=5 into the second equation gives us 3(5) + 1 = 16.

Explanation

To solve the first equation, we add 7 to both sides to get 2x = 10, then divide by 2 to find x = 5. Plugging x=5 into the second equation gives us 3(5) + 1 = 16.

6. What is the measure of an angle whose supplementary angle is 150°?

45°

Two angles are said to be supplementary if the sum of their measures is 180°. 180 – 150 = 30. Therefore, the measure of the angle described in the question is 30°.

60°

90°

Two angles are said to be supplementary if the sum of their measures is 180°. 180 - 150 = 30. Therefore, the measure of the angle described in the question is 30°.

Explanation

Two angles are said to be supplementary if the sum of their measures is 180°. 180 - 150 = 30. Therefore, the measure of the angle described in the question is 30°.

7. If four boxes of books each weighing at least 20 pounds have an average weight of 60 pounds, and if one of the boxes weighs 80 pounds, what is the maximum possible weight of the heaviest box in pounds?

The maximum possible weight of the heaviest box is 140 pounds.

The maximum possible weight of the heaviest box is 80 pounds.

The maximum possible weight of the heaviest box is 100 pounds.

There are four boxes and the average weight is 60 pounds, so the total weight of all four boxes is 4 × 60, or 240 pounds. One of the boxes must weigh 80 pounds, so the remaining three boxes total 240 – 80, or 160 pounds. To find the maximum weight of the heaviest remaining box, the two others must be the minimum weight, which is 20 pounds. Therefore, the maximum possible weight of the heaviest box is 160 – 20 – 20, or 120 pounds.

To find the maximum weight of the heaviest remaining box, the two others must be the minimum weight, which is 20 pounds. Therefore, the maximum possible weight of the heaviest box is 160 - 20 - 20, or 120 pounds.

Explanation

To find the maximum weight of the heaviest remaining box, the two others must be the minimum weight, which is 20 pounds. Therefore, the maximum possible weight of the heaviest box is 160 - 20 - 20, or 120 pounds.

8. If a = 2b and 4b = 6c, then a =

5c

4c

The second equation can be written as 2(2b) = 6c. Because 2b = a, you can plug a into the equation to get 2a = 6c. Then divide both sides by 2 to get a = 3c.

2c

The correct solution involves substituting the values of a and b into the equations to simplify and find the relationship between a and c.

Explanation

The correct solution involves substituting the values of a and b into the equations to simplify and find the relationship between a and c.

9. Given that 3x + 8y = 43 and 3x - 7y = 13, find the value of y.

Y = 3

. Subtract the second equation from the first equation to get rid of the x variable. Subtracting the y terms gives you 15y (8y – (–7y)) and subtracting the numbers gives you 30 (43 – 13). The equation then becomes 15y = 30. Divide both sides by 15 to get y = 2.

Y = 4

Y = 1

Subtracting the second equation from the first equation eliminates the x variable, resulting in 15y = 30 when subtracting the y terms and numbers. Dividing both sides by 15 yields y = 2.

Explanation

Subtracting the second equation from the first equation eliminates the x variable, resulting in 15y = 30 when subtracting the y terms and numbers. Dividing both sides by 15 yields y = 2.

10. The expression 4! is equal to

The expression 4! equals 120

The expression 4! is undefined

The expression 4! equals 16

The expression 4! is a factorial. To find the value, multiply the number by every positive whole number beneath it: 4 × 3 × 2 × 1 = 24.

Factorial is the product of an integer and all the integers below it. Therefore, the correct answer is to multiply 4 by every positive whole number beneath it: 4 x 3 x 2 x 1 = 24.

Explanation

Factorial is the product of an integer and all the integers below it. Therefore, the correct answer is to multiply 4 by every positive whole number beneath it: 4 x 3 x 2 x 1 = 24.

11. Find the factors of x^3 - 2x^2 - 35x.

X(x - 5)(x + 7)

X(x + 7)(x + 5)

X(x - 5)(x - 7)

First, factor out an x to get x(x2 – 2x – 35). Then factor the quadratic. It factors to (x – 7)(x + 5). Therefore, the factors of the expressions are x(x – 7)(x + 5).

First, factor out an x to get x(x^2 - 2x - 35). Then factor the quadratic. It factors to (x - 7)(x + 5). Therefore, the factors of the expressions are x(x - 7)(x + 5).

Explanation

First, factor out an x to get x(x^2 - 2x - 35). Then factor the quadratic. It factors to (x - 7)(x + 5). Therefore, the factors of the expressions are x(x - 7)(x + 5).

12. What is the difference between the surface area and the volume of a cube with a side of 4?

40

Find the surface area first. The area of one face is 4 squared, or 16. Multiply this by 6 because there are six faces: 16 × 6 = 96. Next find the volume: 4 × 4 × 4 = 64. Now subtract to get the difference: 96 – 64 = 32.

16

24

To find the difference between surface area and volume, first calculate the surface area (96) and volume (64) separately based on the given side length of 4. Then subtract the volume from the surface area to get the difference, which is 32.

Explanation

To find the difference between surface area and volume, first calculate the surface area (96) and volume (64) separately based on the given side length of 4. Then subtract the volume from the surface area to get the difference, which is 32.