ASVAB Practice

The expression "5 factorial" equals A. 125. B. 120. C. 25. D. 10.

. The product of all integers from 1 to x is called the x factorial. The product of all numbers from 1 to 5 is 5 factorial. Thus (5)(4)(3)(2)(1) = 20 (3)(2)(1) = 60 (2)(1) = 120 (1) = 120 The expression 5 factorial" is equal to 120

Which of the following is the smallest prime number greater than 200? A. 201. B. 205. C. 211. D. 214.

1. A prime number is a number larger than 1 that has only itself and 1 as factors. (It can be evenly divided ony by itself and by 1.) 201 is divisible by 3; 205 is divisible by 5; 211, however, is a prime number.

In a regular hexagon, all the angles are equal and one of them is 120 degrees. What is the sum of all the angles of the regular hexagon? A. 240 degrees B. 480 degrees C. 720 degrees D. 360 degree

720

A park commissioner designs a new playground in the shape of a pentagon. If he plans to have a fountain at every corner of the park, how many fountains will there be? A. 4 B. 5 C. 6 D. 7

A pentagon is a five-sided figure. If the park commissioner places a fountain at every corner of the park, there will be 5 fountain

What is the reciprocal of 5/3? A. 0.6 B. 1 and 2/3 C. 2 D. 1

A. 0.6

If you divide 24x³ + 16x² - 8x by 8x, how many x's will be there in the quotient? A. 0 B. 5 C. 2 D. -1

An easy way to do this example is to break it into three examples, dividing each term by 8x. Divide the numbers first, and then the letters. However, to divide the exponentsfor 'x', just find the difference between them. (Thus, x³ / x = x³-² = x².) 24x³/8x + 16x²/8x - 8x/8x = 3x² + 2x - 1 Since the equation asks only how many x's there are in the quotient (not how many x²'s), the answer is 2.

What is the meaning of the statement -30 < -5? A. 30 is greater than 5. B. 30 is less than minus 5. C. Negative 30 is less than negative 5. D. Negative 30 is greater than negative 5.

C. Negative 30 is less than negative 5...In deciding whether a number is greater of less than another, it helps to use a number line. -------.-------.-------.-------.-------.-------.-------.-------.------.------.------.------ __-30___-25__-20__-15__-10__-5____0___5___10__15___20 On the number line above, -5is to the left of 0 and is, therefore, less than 0, but -50 is to the left of -5. This makes -30 less than -5. The < sign is a symbol of inequality, meaning "less than". The statement (-30 < -5) means "negative 30 is less than negative 5."

A length of chain is 5 feet, 3 inches long. If a piece 3 feet, 9 inches in length is cut from the chain, what is the length of the remaining piece? A. 2 feet, 6 inches B. 1 foot, 1 inch C. 1 foot, 4 inches D. 1 foot, 6 inches

D. 1 foot, 6 inches

What is the product of (3a - 2) and (a + 3)? A. 4a + 1 B. 3a² - 6 C. 3a² - 2a - 6 D. 3a² + 7a - 6

D. 3a² + 7a - 6

Divide 15a³b²c by 5abc. A. 10abc B. 3abc C. 5a²b² D. 3a²b

Divide only similar terms. First divide numbers, then letters. When dividing powers of a letter, just subtract the exponents. (15a³b²c)/5abc = 15/5 • a³/a • b²/b • c/c = 3a²b

If one of the angles of a right triangle is 30 degrees, what are the other two angles? A. 30 degrees, 120 degrees B. 60 degrees, 45 degrees C. 60 degrees, 90 degrees D. 45 degrees, 90 degrees

Every right triangle contains an angle of 90 C. 60 degrees, 90 degrees. This particular right triangle also has an angle of 30 C. 60 degrees, 90 degrees. To find the third angle, subtract the sum of these two angles from 180 degrees. 180 - (30 + 90)) = 180 - 120 = 60 degrees in third angle. The other two angles are 60 and 90 degree

A woman has $500 in a bank account. Every week, she writes out a check for $50. If she doesn't make any new deposits, what will her bank account hold x weeks from now? A. $500 + $50x B. $500 - $50x C. $500 - x D. $500 + $50 + x

In x weeks, she will make out checks tor x times $50, or $50x. To find out how much she still has after writing these checks, she would subtract $50x from $500. Thus her bank account will hold $500 - $50x

What is the product of (a - 5) and (a + 3)? A. a² - 15 B. a² + 2a - 15 C. a² - 2a - 15 D. a² - 2

Set this up as a multiplication example in arithmetic. Remember that when you multiply terms with unlike signs, the product has minus sign. (a - 5) • (a + 3) = a² + 3a - 5a - 15 = a² - 2a - 15

Smith Township has a public pool in the shape of a quadrilateral. If the town wants to put a lifeguard on each side of the pool, how many lifeguards are needed? A. eight B. six C. four D. threee

Since a quadrilateral is a four-sided figure, the township will need four lifeguards. (If the sides of a quadrilateral are parallel, it is also called a parallelogram. If all four sides are equal and all four angles are right angles, it is called a square.)

Solve for 'x': 3x + 2 = -13 A. x = 13 B. x = -4 and 1/3 C. x = 8 D. x = -5

Step 1: Subtract 2 from each side of tthe equation in order to eliminate + 2 from the left side. (You are undoing the addition.) 3x + 2 - 2 = -13 - 2 3x = -15 Step 2: Now divide each side by 3 to find x. (You are undoing the multiplication.)3x/3 = -15/3 x = -5

What is the value of (0.1)³ ? A. 0;.3 B. 0.003 C. 0.1 D. 0.001

The exponent in (0.1)³ means you use 0.1 as a multiplier 3 times. (0.1)³ = (0.1) (0.1) (0.1) = 0.001 When multiplying decimals, count off one decimal place in the answer for each decimal place in the numbers you multiply.

If 5x = 30, then x is equal to A. 150 B. 25 C. 6 D. 0.6

The statement 5x = 30 means "5 times a certain number is equal to 30." To find the number, divide each side by 5. This is to undo the multiplication. 5x/5 = 30/5 x = 6

What is the value of (+2)(-5)(+3)(-3)? A. +90 B. +60 C. -13 D. -3

To find the product of more than two numbers, work on only two numbers at a time. If both of these numbers have plus sign (+), their product has a plus sign. If both have minus signs (-), their product has a plus (not a minus) sign. But if hteir signs are different, the product has a minus sign. (+2) (-5) (+3) (-3) = (-10) (+3) (-3) = (-30) (-3) = +90

A cylindrical can has a radius of 7 inches and a height of 15 inches. How many gallons of milk can it hold? (There are 231 cubic inches in a gallon.) A. 15 gallons B. 14 gallons C. 140 gallons D. 10 gallons

To find the volume (V) of a cylinder, multiply π times the square of the radius (r) times the height (h). V = π • r² •h V = 22/7 • 7/1 • 7/1 • 15/1 V = 154 • 15 V = 2,310 (cubic inches (volume) To find the number of gallons this cylinder will hold, divide its volume by 231. 2,310 / 231 = 10 gallons

What is the value of x in the equation x/2 = 7? A. x = 14 B. x = 3½ C. x = 9 D. x = 5

To solve for x in this equation, multiply both sides by 2. This is to undo the division. 2 • (x/2) = 2 • 7 x = 14

from 8x² - 7x subtract 2x - 3x². A. 11x² - 9x B. 5x² - 5x C. 6x² - 4x D. 10x² - 10x

A. 11x² - 9x

If x = 3, what is the value of |x - 7|? A. 4 B. -4 C. 10 D. -10

A. 4

Mr. Larson drove his car steadily at 40 miles per hour for 120 miles. he then increased his speed and drove the next 120 miles at 60 miles per hour. What was his average speed? A. 48 miles per hour B. 52 miles per hour C. 50 miles per hour D. 46 miles per hour

A. 48 miles per hour

What is the product of (z + 2) (2z - 3)? A. 3z - 6 B. z + 4z - 3 C. z² + 4z - 6 D. 2z² + z - 6

An easy way to perform the multiplication is to do four separate multiplications. Then the procedure looks like ordinary miltiplication in arithmetic. Use the FOIL (z + 2) (2z - 3) 2z² - 3z + 4z - 6 2z² + z - 6

A worker can do 1/3 of a job by herself in one day, and her helper can do 1/5 of the job by himself in one day. What portion of the job can they do if they work together for one day? A. 1/4 B. 8/15 C. 1/8 D. 2/15

B. 8/15

An architect designs two walls of a museum to meet at an angle of 120 degrees. What is an angle of this size called? A. acute B. obtuse C. right D. straight

B. obtuse

Solve the following inequality. x + 5 > 7 A. x = 2 B. x > 2 C. x - 7 > 5 D. x - 5 > 7

B. x > 2

Solve for z: 3z - 5 + 2z = 25 - 5z A. z = 0 B. z = 3 C. z = -3 D. no solution

Begin by combining like terms. 3z - 5 + 2z = 25 - 5z 5z - 5 = 25 - 5z Next add 5z to each side to eliminate the -5- from the right side. 5z - 5 + 5z = 25 - 5z + 5z 10z - 5 = 25 Now add 5 to each side to undo the remaining subtraction. 10z - 5 + 5 = 25 + 5 10z = 30 z = 3

Solve for "x": 2x + 6 = 12 - x. A. 6 B. 9 C. 2 D. 3

C. 2

Solve for x: x² = 3x + 10 A. x = 3; x = 10 B. x = -3; x = -10 C. x = -2; x = 5 D. x = 2; x = -5

C. x = -2; x = 5

Solve for x: 8x - 2 - 5x = 8. A. x = 1.3 B. x = 2½ C. x = 3 and 1/3 D. x = -7

C. x = 3 and 1/3.. To solve for x, combine all similar terms, and set the equation equal to zero. (8x - 5x) + (-2 - 8) = 0 Do the operations inside the parenthesis. 3x - 10 = 0 Next, add 10 to each side. You are undoing the subtraction. 3x - 10 + 10 = 0 + 10 3x = 10 Finally, divide each side by 3 to find the value of x> You are undoing the multiplication.

If 40% is equal to the fraction x/30, what is the value of x? A. 0.4 B. 15 C. 1,200 D. 12

Change 40% to a decimal and write an equation to solve for x. 0.4 = x/30 Multiply both sides by 30. You are "undoing" the division.

Which of these is a cylinder? A. a stick of butter B. an orange C. compact disc D. a frozen juice can

D. a frozen juice can

How many cubic yards of concrete are needed to make a cement floor that is 9 feet by 12 feet by 6 inches thick? A. 2 B. 18 C. 54 D. 648

First change all measurements to yards 9 feet = 3 yards; 12 feet = 4 yards; 6 inches = 1/6 yard To find the volume of the concrete, multiply the length by the width by the height. 3 • 4 • 1/6 = 12 • 1/6 = 2 cubic yards

Ten ounces of qiluid 20% fruit juice and 80% water. The mixture is diluted by adding 40 additional ounces of water. What is the percentage of fruit juice in the new solution? A. 4% B. 10% C. 20% D. 40%

First find how many ounces of the original mixture were fruit juice. 10 • 20 = 10 • .2 = 2 ounces. Next find the total number of ounces in the new mixture. 10 + 40 = 50 ounces Then find what part of the new mixture is fruit juice, and convert it to a percentage. 2/50 = 1/25 = 4/100 = 4%

A wildlife preserve is laid out in the shape of a perfect circle whose radius is 14 miles. The lions' territory in this preserve is shaped like a wedge and has a fence around it. Two inner sides of a fence meet at a 90-degree angle in the center of the preserve. How much territory do the lions have? A. 140 square miles B. 3½ square miles C. 210 square miles D. 154 square miles

First find the area of the entire wildlife preserve. Since it is a circle, use the formula for the area of a circle. (Area equals π times the square of the radius.) A = π •R² = 22/7 • (14)² = 22/7 • 196 = 22 • 28 = 616 square miles The lions' territory is a wedge formed by a 90-degree angle at the center of the circle. Since a circle has 360 degrees, we can find the part of the preserve inhabited by lions. 90/360 = 1/4 Next find what equals in square miles. 1/4 • 616/1 = 154 square miles

A room is 19 feet long, 10 feet wide, and 8 feet high. If you want to paint the walls and ceiling, how many square feet of surface will you have to cover with paint? A. 232 square feet B. 422 square feet C. 464 square feet D. 654 square feet

First, find the area (surface) of the ceiling. Since it is opposite the floor, it has the same length and width (A = I • w). 19 feet • 10 feet = 190 square feet (ceiling) Next find the combined area of twomatching (opposite) walls. Start with the walls formed by the length and hight of the room. 19 feet • 8 feet = 152 square feet (first wall) 152 feet • 2 = 304 square feet (matching walls) Then find the area of the walls formed by the width and height of the room. 10 feet • 8 feet = 80 square feet (second wall) 80 feet • 2 = 160 square feet (matching walls) finally, combine all surfaces to be painted. 190 + 304 + 160 = 654 square feet.

How many inches are contained in 'f' feet and 'i' inches? A. f • i B. f + i C. f + 12i D. 12f + i

In 1 foot, there are 12 inches (12 • 1). In 2 feet, there are 24 inches (12 • 2). Therefore, in 'f' feet, there are 12 • f or 12f inches. Add 12f inches to i inches to obtain the total of 12f + i.

One of the equal angles of an isosceles triangle is 40 degrees. What is the angle opposite the unequal side? A. 40 degrees B. 90 degrees C. 100 degrees D. 140 degrees

In an isosceles triangle, two of the sides are equal. This means that the angles opposite them are equal, too. If one is 40 degrees, then so is the other. To find the angle opposite the unequal side, begin by adding the equal angles. 40 + 40 = 80 degrees To find the third angle, subtract this amount from 180 (the number of degrees in any triangle). 180 - 80 = 100 degrees (third angle)

An artist sold 4 of his paintings. These represented 0.05 of all the artwork he had done. How many paintings had he made? A. 100 B. 80 C. 50 D. 20

Let p stand for the number of paintings the artistt made. The 4 paintings he sold are equal to 0.05 of all his paintings. This can be expressed as an equation. 0.05p = 4 To solve for 'p', divide both sides by 0.05. You are undoing the multiplication of 0.05 and 'p'. 0.05p/0.05 = 4/0.05 (Clear the decimal in the divisor.) 1p/1 = 400/5 p = 80 (paintings made)

Find the square root of 85 correct to the nearest tenth. A. 9.1 B. 9.2 C. 9.3 D. 9.4

One way to solve this is to square each of the suggested answers to see which is close to 85. Thus 9.1 • 9.1 = 82.81 9.2 • 9.2 = 84.64 9.3 • 9.3 = 86.49 9.4 • 9.4 = 88.36 To find squares of 9.2 and 9.3 are near 85. Find the difference between the square of each of these numbers and 85. (9.2) 85.00 - 84.64 = 0.36 (9.3) 86.49 - 85.00 = 1.49 The square 9.2 is closer to 85 than the square 9.3. Therefore, the square root of 85, to the nearest tenth, is 9.2

Find the value of (-3) to the 4 power + (-2) to the 4 power + (-1) to the 4 power. A. 98 B. -98 C. -21 D. 21

Solve by doing each arithmetic operation and combining answers. Remember that the product of two negative or two positive numbers is a positive number. The product of a negative and a positive number is negative (-3) to the 4 = (-3)(-3)(-3)(-3) = 81 (-2) to the 4 = (-2)(-2)(-2)(-2) = 16 (-1) to the 4 = (-1)(-1)(-1)(-1) = 1 ----- 98

If the largest possible circular tabletop is cut from a square whose side is 2 feet, how much woods is wasted? (Use 3.14 for π.) A. 1 squarre foot B. 1.86 square feet C. 5.86 square feet D. 0.86 square feet

Step 1: Find the area of the square. 2 feet • 2 feet = 4 square feet Step 2: Find the area of a circle, using the formula A = π • R². (The radius equals half the diameter; the diameter of this circle is 2 feet - the same length as one side. of the square.) 3.14 • 1² = 3.14 square feet Step 3: Subtract 3.14 square feet from 4 square feet to find the wood that is wasted, 0.86 square feet.

If a car traveled 200 miles at an average rate of speed of 'r' miles per hour, the time it took for the trip could be written as A. 200/r B. r/200 C. 200r D. r/60

The basic formula for travel is "distance equals rate multiplied by time," or D = rt. The car traveled 200 miles (D); therefore 200 = rt. To solve for 't' (time), divide both sides of the equation by r. (You are undoing the multiplication.) 200/r = rt/r 200/r = t (time it took for trip)

My average grade on a set of five tests was 88%. I can remember only that the first four grades were 78%, 86%, 96%, 94%. What was my fifth grade? A. 88 B. 86 C. 84 D. 82

The easiest way to solve this is to form an equation using x as the unknown grade. (78 + 86 + 96 + 94 + x) / 5 = 88 (354 + x) / 5 = 88 Multiply both sides by 5. This is to undo the division. 5 • [(354 + x) / 5] = 88 • 5 Simplify both sides of the question. 354 + x = 440 x = 440 - 354 x = 86 (grade)

Two circles have the same center. It their radii are 7 inches and 10 inches, find the area that is part of the larger circle but not the smaller one. A. 3 square inches B. 17 square inches C. 51π square inches D. 70π square inches

The formula for the area of a circle isπ • R². Find the area of the lartger circle first. π • 10² = 100π square inches. Then find the area of the smaller circle. π • 7² = 49π square inches. To find the part of the larger circle that the smaller one doesn't touch, subtract the two areas. 100 - 49 = 51π square inches.

An equilateral triangle has the same perimeter as a square whose side is 12 inches. What is the length of a side of the triangle? A. 9 inches B. 12 inches C. 18 inches D. 16 inches

The perimeter of a square is 4 times a side. Therefore, the perimeter of this square is 4 • 12 feet or 48 feet. The equilateral triangle has the same perimeter as the square. Since the 3 sides of an equilateral triangle are equal, divide by 3 to find the length of one side. (48 feet) ÷ 3 = 16 feet (length of one side)

A 10-foot-high ladder is resting against an 8-foot-high wall surrounding a tennis court. If the top of the ladder is exactly even with the top of the wall, how far is the base of the ladder from the wall? A. 18 feet B. 6 feet C. 12 feet D. 9 feet

The wall, the ladder, and the ground in the tennis court form a right triangle. he ladder is on a slant, and is opposite the right angle formed by the wall and the ground. In this position, the ladder is the "hypotenuse" of the triangle. In geometry, the Pythagorean Theorem states that the square of the hypotenuse (c²) equals the sum of the squares of the other two sides (a² + b²). Thus, a² + b² = c² 8² + x² = 10² Solve by doing the arithmetic operations, and by clearing one side of the equation for x². 64 + x² = 100 x² = 100 - 64 x² = 36 Then find the square root of x² and 36. x = 6 The base of the ladder is 6 feet from the wall.

if b - 3 = 7, then b is equal to A. 10. B. 4. C. 21. D. 8.

This equation means "a number, decreased by 3, is equal to 7" b - 3 = 7 To arrive at a true statement for b, we want to eliminate -3 on the left side of the equation. We do this by adding 3. (This in undoing the subtraction.) We then add 3 to the other side so that the statement remains an equation. (b - 3) + 3 = 7 + 3 By simplifying both sides, we isolate 'b' and thus find the solution. b = 10

What is the result of subtracting 3x² - 5x - 1 from 8x² + 2x + 9? A. 5x² - 3x - 10 B. -5x² - 3x - 10 C. 5x² +7x - 8 D. -5x² - 7x + 8

To subtract one polynomial from another, you change the signs of the terms in the subtrahend. First write the example as a subtraction in arithmetic. (From) 8x² + 2x - 9 (Take) 3x² - 5x - 1 Then change the signs of the terms in the bottom row (the subtrahend) and combine terms that are alike. 8x² + 2x - 9 -3x² + 5x + 1 ___________ 5x² + 7x - 8

A good rule of thumb is that a house should cost no more than 2½ times its owner's income. How much should you be earning to afford a $64,000 home? A. $20,500 B. $25,000 C. $32,000 D. $160,000

Use m as the owner's income. According to the rule of thumb, a house costing $64,000 should be no more than 2½ times an owner's income, or 2½m (2.5m). This can be stated as an equation. 2.5m = $64,000 To solve for m, divide both sides by 2.5. You are undoing the multiplication. 2.5m/2.5 = $64,000/2.5 (Clear the decimal in the divisor.) m = $640,000/25 = $25,600 (Owner's income)

When the temperature is 20ºC, what is it the Fahrenheit (F) scale? (Use the following formula). F = (9/5 • C)+32 A. 93 and 3/5 degrees B. 78 degrees C. 62 and 7/5 degrees D. 68 degrees

degrees..Use the formula F = (9/5 • C) + 32 Substitute 20 degrees for C. F = (9/5 • 20) + 32 F = 36 + 32 = 68 degrees.

The perimeter of a rectangle is 38 inches. If the length is 3 inches more than the width, find the width. A. 17½ inches B. 8 inches C. 11 inches D. 14½ inches

inches..The perimeter of a rectangle is the sum of its four sides. If x equals its width, then x + 3 equals the length. (The length is 3 inches more than the width.) From this, you can write an equation to find the perimeter. (Use the formula 2w + 2l = P.) x + x + (x + 3) + (x + 3) = 38 To solve for x, combine similar terms. 4x + 6 = 38 4x = 38 - 6 4x = 32 x = 8 (inches)