ASVAB: Arithmetic Reasoning Questions, *THIS ONE* ASVAB 2020 Arithmetic Reasoning

7 x 6

42

7 x 6 =

42

12 x 4 =

48

8 x 6

48

8 x 6 =

48

Jim bought an electric power drill at 75% of the regular price. He paid $34.00 for the drill. What was the regular price of the drill? a. 100 b. 136 c. 150 d. 144

$34 is 25% of what number?

What is a radius?

half the diameter

12 x 12

144

How to set up division of 10.47 / 87.67

top goes in the house Numerator divided by the denominator

WHAT NUMBER GOES IN THE HOUSE 9.440 / 2.95

FIRST NUMBER GOES IN THE HOUSE

how to add decimals

1. line up the decimals 2. fill in spaces with zeroes (0) 3. bring decimal STRAIGHT DOWN 4. Add using correct place value

Denise buy a soda for 90c, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5% sales tax, how much changes would she receive from a $10 bill? a)$6.13 b)$5.75 c)$5.25 d)$4.82

1.20 .90 + 2.90 -------- 5.00 5 x 3.5% = 5 x .035 = 175 = .175 = .18c *convert percent into decimals, move over TWO times* 10.00 - 5.18 = 4.82

What is a factorial?

A factorial is the product of an integer and all the integers below it. Factorials are symbolized with an exclamation point. To find the factorial 6 (or 6!), you would multiply 6 × 5 × 4 × 3 × 2 × 1 to get 720.

Formula for circumference of a circle

C = 2πr or C = πd

Equivalent proportions

Equivalent proportions are ratios that are set equal to one another. It is crucial to make sure that the numerator of the left-hand side ratio represents the same thing as the numerator of the right-hand side ratio; and, the denominators of each ratio must also represent the same thing:

What is prime factorization?

Finding all the prime factors

HOW TO CALCULATE PERCENT INCREASE: THE RENT RAISED FROM $900 TO $972, WHAT WAS THE PERCENT INCREASE?

INCREASED AMOUNT / ORIGINAL AMOUNT = N / 100

what is the simple interest formula?

Interest = (principal)(rate)(time) prt

How do you clear the fraction when solving for x? x/3 - 7 = 15x

Multiply EVERYTHING by 3

What is the formula for probability of two or more events ex. What is the probability of rolling a 4 on a six sided die twice?

P (A and B) = P(A) x P(B)

What is the probability of non-exclusive events

P(A or B) = P(A) + P(B) - P(A and B)

what is the probability of exclusive events?

P(A) + P(B)

What is a diameter?

The line from one side to the other that goes through the center or 2 times the radius (r) D = 2r

HOW TO SOLVE UNIT RATIO PROBLEMS

UNIT (AMOUNT) / TOTAL GIVEN

Will has been working on a report for 4 hours each day, 7 days a week for 2 weeks. How many minutes has Will worked on his report?

X BY 2 WEEKS, NOT 14 DAYS If Will has worked 4 hours per day for 7 days per week, he has worked 4(7) = 28 hours per week. He did this for 2 weeks, so he has worked 28(2) = 56 hours in the 2 weeks. Multiply by 60 to convert this to minutes. 56(60) = 3,360 minutes.

|5| = 5 |−20| = 20 |5 − 12| = |−7| = 7 is considered what?

absolute values

20 - (-5) = __. (a) -25 (b) 25 (c) 15 (d) -15

(b) 25 Subtracting a negative number is the same as addition, so 20 - (-5) is really 20 + 5 = 25.

Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon of gasoline and gasoline cost $1.25 per gallon, what was the cost in dollars of the gasoline for the trip? (a) $20.00 (b) $24.00 (c) $25.00 (d) $40.00

(c) $25.00 Ms. Smiths Car can go 35 miles per gallon, to go 700 miles she will need 700/35, or 20 gallons. $1.25 x 20 gallons is $25.00

A farmer constructs a wooden bin. The bin is 6 feet long, 4 feet wide, and 3 feet ft deep. The bin rests on the legs that are 3.5 feet tall to keep the grain away from the damp ground. How much grain can the farmer store in his new bin? a) 62 cubic ft b) 72 cubic ft c) 82 cubic ft d) 91 cubic ft

*the leg height is irrelevant* This is a question about volume. volume of a rectangle is v = L x W x H v = 6 x 4 x 3 v = 24 x 3 v = 72 cubic ft

June's Weekly salary is $70 less than Kelly's, which is $50 more than Eileen's. If Eileen earns $280 per week, how much does June earn per week? (a) $160 (b) $260 (c) $280 (d) $300

-Eileen earns $280 a week -Kelly earns $50 more than Eileen, so $280 + $50 = $330 -June earns $70 less than Kelly, so $330 - $70 = $260

What are your odds of selecting a red card twice in a row from a standard deck of playing cards. Assume you don't replace a card after making your first selection. There are 13 of each set of cards

13 + 13 = 26 total red cards 26/52 x 25/51

different ways to express ratios

18/5 = 18:5

Andy took his girlfriend out to dinner. If dinner costs $25.10, Andy gave a 20 percent tip, and he gave the waitress a $40. how much change should he get back?

25.10 x .2 $5.02 25.10 + 5.02 = 30.12 total $40.00 - 30.12

how many feet are in a yard?

3 feet

3/50 =

3/50 = .06 = 6%

How many quarts are in a gallon?

4 quarts in a gallon

7 x 7

49

How do you set up: A cake recipe calls for 5 cups of flour for baking 2 cakes. How many cups of flour are needed to bake 7 cakes?

5 cups over 2 cakes = 2.5 cups. 2.5 x 7 = 17.5

Ratios can also be written as fractions. 5:8 can be written how as a fraction?

5/8

9 x 6=

54

A display selling bunches of bananas contains six dozen banana bunches when the display is full. The manager of the product department is supposed to make sure the display is restocked when it is one quarter full. How many bunches of bananas will be on display when it's time to restock? a) 10 b) 18 c) 20 d) 24

6 (bananas) x 12 (dozen) = 72 72 x 1/4 (one quarter full) = 72/4= 24

Solve 6!

6! = 6 x 5 x 4 x 3 x 2 x 1 to get 720

8 x 8 =

64

9 X 9

81

13% OF 100

= 13

A floor is made up of hexagonal tiles, some of which are black and some of which are white. every black tile is completely surrounded by white tiles. how many white tiles are there around each black tile? a. four b. five c. six d. eight

A hexagon has 6 side. each of the six sides of the black tile must touch a side of the white tile, so there are six white tiles surrounding each black tile.

A number raised to the power of 0 equals __

A number raised to the power of 0 equals 1

Solve 6⁰

A number raised to the power of 0 equals 1. For example: 6⁰ = 1

A number raised to the power of 1 equals __

A number raised to the power of 1 equals itself.

Solve 6¹

A number raised to the power of 1 equals itself. For example: 6¹= 6

When multiplying two powers with the same base, you can __ the exponents. A. ADD B. MULTIPLY C. DIVIDE D. NEITHER

A. When multiplying two powers with the same base, you can add the exponents. For example: 6³ × 6⁴= 3+4= 6⁷

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

A. x + x + 8 = 70, solve for x. x = 31

What is the area of a rectangle?

A=lw

formula for area of a rectangle

A=lw

What is a proportion?

An equation stating that two ratios are equal. they are solved using the cross product rule

Multiples of 4

An integer is divisible by 4 if the last two digits form a multiple of 4

For all positive values of x < 50, how many values are divisible by both 3 and 5?

Any number divisible by both 3 and 5 must be divisible by 3 x 5 since 3 and 5 are both prime numbers. Thats 15, which is the smallest number. add another 15 to 15 to find the next number, 30. then add another 15, which equals 45. The next number would be 60 but that's about the range. So there are 3 possible values: 15, 30, 45.

If it costs $5.50 per square foot to build a new patio, how much would it cost to build a patio that is 9 by 20 feet? a) $647 b) $789 c) $878 d) $990

Area of a rectangle A = L x W A = 20 x 9 = 180 180 x 5.5 = $990.00

A security guard walks the equivalent of six city blocks when he makes a circuit around the building. If he walks at a pace of eight city blocks every 30 minutes, how long will it take him to complete a circuit around the building, assuming he doesn't run into any thieves? (a) 20.00 minutes (b) 3.75 minutes (c) 22.50 minutes (d) 7.5 minutes

C. Divide 30 by 8 to determine how long it takes to walk one city block = 3.75 minutes. Then multiply by 6 the number it takes to complete the circuit. The answer is 22.5 minutes.

A teacher deposited $3,000 in retirement fund. If she didn't add any more money to the fund, which earns an annual interest rate of 6%, how much money would she have in 1 year? a) $180 b) $3006 c) $3180 d) $6000

Convert percent to decimal 6% = .06 3000 x00.06 ..move decimal 2 places --------- 180.00 **move decimal place back 2 spaces $3000 + $180 = $3180

Jack sets up a security camera in his back yard to take automatic pictures every 15 minutes. If the first picture is taken at 10 pm, and Jack shuts the camera off at 2 am, how many pictures will jack have? a) 16 pictures b) 132 pictures c) 17 pictures d) 15 pictures

Count out problems like this, it doesn't take that long and eliminates mistakes: 10 pm 11:15 10:15 11:30 10:30 11:45 10:45 12 am 11 pm 12:15 12:30 1:45 12:45 2 am 1 am 1:15 1:30 17 pictures were taken

A sales manager buys antacid in bottles the gross. If he goes through 3 bottles antacid everyday, how long will the gross last? (a) 144 days (b) 3 days (c) 20 days (d) 48 days

D. 144 bottles in a gross, and 144 ÷ 3 (bottles per day) = 48 days.

how to solve long division

DONT FORGET TO CARRY DOWN THE NUMBER BEFORE ATTEMPTING TO SOLVE

Forty soldiers in basic training are to undergo hand-to-hand combat training in 60 minute training period, but only ten can be trained at one time. In order for each soldier to get the same amount of training time, how many minutes should each solider be trained? a) 1 1/2 minutes b) 6 minutes c) 30 minutes d) 15 minutes

DONT OVER THINK THIS How many groups of soldiers will there be? 40 soldiers ÷ 10 = 4 groups 4√60 = 15 minutes per group

how to multiply decimals

Does not require aligning the decimal points, arrange with right justification, multiply like normal and then count the number to the right of the decimal and place it accordingly

How to solve hourly wage problems

Dollars / Hours. Find hourly wage the first week, then divide weekly salary by hourly wage

mutually exclusive event vs. non mutually exclusive event

Ex: an exclusive event would be searching for a specific item such as a queen of hearts vs a nonexclusive event such as searching for a heart in a deck of cards (13 card options)

A road map is drawn on the scale of 1 inch equals 10 miles. When planning your trip, you notice that you'll have to travel 10 inches (on the map) to the first turn, 7 inches to the second turn, and then 15 inches to your destination. Your car gets 28 miles per gallon, and gas cost $2.73 per gallon. How much gas money will you need round trip

FIRST OFF, DID YOU NOTICE ROUND TRIP? distance one way: 100 + 70 + 150 = 320 miles Round trip: 640 miles 28 (mpg) √640 (miles) = 22.85 22.85 x 2.73 (gas) --------- $62.41

A cake recipe calls for 5 cups of flour to bake 2 cakes. How many cups of flour will be needed to bake 7 cakes? a) 35 b) 24.5 c) 17.5 d) 12

Find unit ratio, or How many cups are there per cake? 2√5 2.5 (2.5) x 7 cakes = 17.5

An empty 50 gallon barrel weighs 35 pounds. When completely filled with water, the barrel weighs 455 pounds. Assuming these factors to be true, approximately how much is the weight of 1 gallon of water? a) 5.3 pounds b) 6.5 pounds c) 7.8 pounds d) 8.4 pounds

First subtract the weight of the empty barrel from the barrel full: 455 - 35 = 420 divide 420 by 50 gallons = 8.4

The ratio of female nurses to male nurses at a certain hospital is 5 to 3, which is written mathematically as 5:3. What would be the ratio of female nurses to all nurses at that same hospital?

For every 5 female nurses there are 3 male nurses, meaning that for every 8 (male or female) nurses, 5 of them are female. Thus, the ratio of female nurses to total nurses is 5:8.

Mack travels 1,100 miles during a 40-hour workweek. If he spends two-fifths of his time traveling, how many hours does he spend traveling? a) 16 b) 12 c) 22 d) 8

He spending a portion of his time traveling, the distance is irreverent. so think 40 hours x 2/5 40/1 x 2/5 = 80/5 = 16

How to divide fractions

Invert the second fractions (the one doing the dividing) and multiply the numerator together and the denominator together (horizontally) then simplify

On a trip, you drive 350 miles at an average speed of 60 mph. You then return home, driving at an average speed of 70 mph. How long did it take you to complete the trip? a) 8.9 hours b) 9.3 hours c) 10.8 hours d) 11.2 hours

Keep simple and calculate each d = rt 350 = 60(t) 60√350 = 5.8 350 = 70(t) 70√350 = 5 KICK OFF THE ZEROS TO MAKE EASIER

What is Order of Operations?

PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

Solve |4 x 3 - 20| a. -8 b. 8 c. 16 d. 68

Question 3 Explanation: This is an absolute value problem, meaning the answer measures the distance from 0, regardless of whether the answer originally comes out as positive or negative. Start by solving the problem using PEMDAS. Begin with 4×3 which equals 12. Next, subtract 20, which is −8. This is not the final answer, however; the absolute value of −8 is 8, since that's how far it is from 0.

For every 3 female students at a school, there are 5 male students. What is the ratio of female students to all students? a. 3: 5 b. 5: 3 c. 8: 5 d. 3: 8

Question 6 Explanation: There are 3 female students to every 5 male students, but the question asks for the ratio of female students to all students. 3+5=8 and out of those 8 students, 3 of them are female, so the correct ratio is 3:8.

how to solve ratio problems: Rod and Joy own a condo together, which they decide to sell for 200,000. The two decide to split the proceeds according to the ratio of money that each invested in the property. Rod put in the most money, at a ratio of 5:3. How much money should Joy get from the sale?

Ratio problems: add 5 + 3 to find common ground 3:8 is joy 5:8 is Rod 3 / 8 = x / 200,000 cross multiply (200,000)(3) = 8x 600,000 = 8x $75,000

What is a ratio?

Ratios represent the amount of one quantity in comparison to another quantity

How to multiply fractions

Simplify if possible, multiple straight across.

An employee's ratings on performance appraisals for the last three quarters were 92, 88, and 86. If the required years average to qualify for the promotion is 90, how much should the fourth quarter rating be? A. 90 b. 93 c. 92 d. 94

Solve for x in an average formula

multiples of 3

The Rule for 3: A number is divisible by 3 if the sum of the digits is divisible by 3 This means that we need to add up the digits in the number and see of the answer is can be divided by 3 without a remainder. Example: 34,911 Step 1: Add up the digits. 3 + 4 + 9 + 1 + 1 = 18

Multiples of 6

The Rule for 6: The prime factors of 6 are 2 and 3. So for a number to be divisible by 6, it must also be divisible by 2 and 3. Therefore, we need to check if a number is even and then check if the sum of the digits is divisible by 3. Example: 23,908 Step 1: Determine if the number is even. It ends in 8, so this number is even. Therefore it is divisible by 2. Step 2: Add the digits together. 2 + 3 + 9 + 0 + 8 = 22 Step 3: 3 does not divide evenly into 22. So this number is not divisible by 3. Step 4: Because this number is only divisible by 2, and not by 3, it is NOT divisible by 6.

Multiples of 9

The Rule for 9: The prime factors of 9 are 3 and 3. So we can use a very similar rule to determine if a number is divisible by 9. Basically, we will see if the sum of the digits is divisible by 9. If it is, then the actual number is also divisible by 9. Example: 871,989 Step 1: Add up the digits. 8 + 7 + 1 + 9 + 8 + 9 = 42. Step 2: Determine if 9 goes into 42 evenly. We know that 9 x 4 = 36 and 9 x 5 = 45. So 9 will not go into 42 evenly. Step 3: 871,989 is not divisible by 9.

How to convert percentages to decimals

The percentage symbol, %, literally means "per hundred (100)". So, 12% means "12 per 100". We can write "12 per 100" as the fraction 12/100. or .12

Solve for x in an Inequality 5x + 15 ≥ 50

The process of solving for x in an inequality is nearly the same as it is in an equality. The difference is that when you divide (or multiply) by a negative number, the inequality sign changes direction.

The average of x and y is 30. If z = 15, what is the average of the three terms x, y, and z? a) 3 b) 15 c) 25 d) 30

To find the average of the three terms, first find the sum of the terms and then divide by 3. Theres no way to know the exact terms of x and y, but we do know the average of the two terms is 30, so the sum must be 2(30) = 60. Since z = 15, then the sum of the three terms is 60 + 15 = 75. Lastly, divide by 3 to get 25.

A postal carrier can deliver mail to about 900 addresses in one day. In the city, there are 26,942 residents. Workforce policies require hiring 5% more carriers than are estimated to be needed in order to compensate for vacation, sick days, and so on. About how many mail carriers must be hired to deliver mail to all of the Hewitt citizens each day? a. 29 b. 30 c. 31 d. 32

To increase something by 5%, it would be 105%, not .05%, duh!

what is the percent change formula? For example: A $200 watch is on sale for $160. What is the percent change in the price of the watch? a. 25% decrease b. 20% decrease c. 20% increase d. 25% increase

Using the formula for percent change, divide the actual change by the original amount. Since the watch was originally $200 and during the sale it is $160, the watch decreased in price by $40. Divide $40 by the original amount of $200 to get .2 or 20%

Volume of a cube formula

V=s^3

what is the formula for volume in a cylinder

V=πr²h, where r is the radius of the circular base and h is the height

Rosita buys 300 feet of yarn for a craft project. If the yarn costs 12 cents a yard, how much does Rosita spend? a) $36.00 b) $1200.00 c) $360.00 d) $12.00

We know: 300 feet of yarn purchased .12 cents a yard - how many feet are in a yard? 3 convert feet to yard 300 ÷ 3 = 100 100 x .12 = $12.00

Timothy runs ever morning once around a circular track in a park. if the radius of the circular track is 50 yards, how far does Timothy run every morning? a) 250 yards b) 285 yards c) 314 yards d) 380 yards

What is the formula for circumference? 2πr 2 x π x 50 = 100 x π = 314 yards

subtracting exponents

When dividing two terms with the same base, combine exponents by subtracting

If you're in a car traveling 50 mph, how far will you travel in 45 minutes?

With problems involving minutes and mph you must first convert minutes to hours 45/60 = 3/4 hr d = rt d = (50) (3/4) 150/4

THE VALUE OF 8^0 = A. 8 B. 0 C. 1 D. -8

X^0 is defined as always equal to 1, provided that x does not equal 0. therefore 8^0 = 1

The prime factors of a number

are the factors broken down into prime numbers

Acrimony most nearly means: a) politeness b) goodwill c) harshness d)civility

c) Harshness of speech

what is the difference between circumference vs area

circumference is around the circle, area is all inside the circle c= 2πr A= πr²

How to solve probability problems

desired/total

A car is headed west for North Platte left at the same time that a char headed east left at the same place. The car headed west for North Platte traveled at 55 miles per hour. The car headed east traveled at 70 miles per hour. How many miles apart were the cars at the end of 2.5 hours? a) 212 miles b) 165.5 miles c) 125 miles d) 312.5 miles

distance = (rate)(time) Because these are opposites traveling away from each other, Set up the problem as one car traveling in one direction. 70 mph + 55 mph = 125 mph rate mph is set up for hours. 125 mph (rate) x 2.5 hours (time) = 312.5 distance

If a coin is flipped three times, what is the probability. that non of the occurrences will result in a head? a) 0 b) 1/8 c) 1/6 d) 1/3

in order to flip a coin 3 times with no heads, the first flip must be a tail and the second flip bust e a tail and the second flip must also be a tail and the third flip must be a tail, too. therefore ½ × ½ × ½ = ¹/₈

What are Cube Roots?

inding a cube root is a lot like finding a square root. Cube root is the inverse of taking the cube of number—in other words, cube root "undoes" cube. Consider: 3√8= 2 = 2 x 2 x 2

volume of a rectangle =

length x width x height

How to set up miles, gas gallon problems?

miles ------ gallons miles/gallons

Formula for sum of arithmetic sequence

n = last number in sequence a1 = first number in sequence an = last number in sequence

Percent change formula for ex: Rebeccas salary of $500 per week increased to $620. What percentage pay raise did she receive? a. 15% b. 10% c. 24% d. 18%

percent change = new amount - old amount / old amount ) x 100

distance =

rate x time d= rt

A model satellite has a scale of 1 cm : 2 m. If the real satellite is 12 m did then how wide is the model satellite? a. 12 cm b. 8 cm c. 9 cm d. 6 cm

scaled / actual size 1/2 = x/12 2x = 12 x = 6

what is the probability of selecting a blue marble in a bag that has 5 green marbles, 9 red marbles, and 6 blue marbles twice in a row? Assume you don't replace a marble after the selection.

subtract 1 from 6/20 to find second changed outcome

what is a rate?

the ratio of two measurements with different units. ex. (km/h)or(m/s)

numerator ------------- denominator

these are the components of a fraction numerator / denominator 3 / 4

what is the combined rate formula?

time/a + time/b = 1

How to set up: Joshua has a jar with 100 marbles. The jar contains twice as many red marbles as yellow marbles, three times as many green as yellow, and twice as many purple as red. How many yellow marbles are in the jar? a) 5 b) 8 c) 10 d) 20

yellow = x red = 2x green= 3x purple= 4x x + 2x + 3x + 4x = 100 Combine like terms 10x = 100 x= 10

common fraction and decimal equivalents

1/3 = 0.3 = 33.3% 2/3 = 0.6 = 66.6% 1/5 = 0.2 = 20% 2/5 = 0.4 = 40% 3/5 = 0.6 = 60% 4/5 = 0.8 = 80% 1/8 = 0.125 = 12.5% 3/8 = 0.375 = 37.5% 5/8 = 0.625 = 62.5% 7/8 = 0.875 = 87.5%

12 x 3 =

12 x 3 = 36

A 2-ton truck is taxed at a rate of $0.12 per pound. How much is the total tax bill? (a) $480 (b) $240 (c) $120 (d) $600

A. 2,000 pounds to a ton. 4,000 × .12 = 480

An office building has 30 employees and provides 42 square feet of work space per employee. If five more employees are hired, how much less work space will each employee have? (a) 6 square feet (b) 7 square feet (c) 7.5 square feet (d) 36 square feet

A. First find the area of the office, 42 ft. × 30 = 1260 sq ft. Then divide the space by 35 employees, each employee now has 36 sq ft of workspace, which is 6 feet less than originally.

MIchael needs 55 gallons if paint to paint an apartment building. He would like to purchase the paint for the least amount money possible. Which of the following should he buy? (a) two 25-gallon buckets at $550 each (b) eleven 5-gallon buckets at $108 each (c) six at 10-gallon buckets at $215 each (d) fifty-five 1-gallon bucket at $23 each

B. Choice (a) doesn't have enough paint (2 ×25 gal = 50 gal) so it's wrong. Choice (b): 11 × $108 = $1,188 Choice (c): 6 × $215 = $1,290 Choice (d): 55 × $23 = $1265

As a member of FEMA, you're required to set up a contingency plan to supply meals to residents of a town devastated by a tornado. A breakfast ration weights 12 ounces and the lunch and dinner rations weight 18 ounces each. Assuming a food truck can carry 3 tons and that each resident will receive 3 meals per day, how many residents can you feed from one truck during a 10-day period? (a) 150 residents (b) 200 residents (c) 250 residents (d) 300 residents

B. First find how many ounces each truck can hold. 2,000lb. are in a ton, so each truck can carry three times that 6,000lb. There are 16 ounces to a pound so one truck can carry 96,000 ounces ( 16oz. × 6,000lb.). Now find the daily total for each persons three meals 12oz + 18oz + 18oz = 48oz. Now 96,000 × 48 = 2,000 daily rations. This rations need to last 10 days (2,000 ÷ 10 = 200) So 200 residents can be fed by one truck for 10 days.

Jenny's test grades are 93,89, 96, and 98. If she wishes to raise her average to 95, what does she need to score on her next test? (a) 100 (b) 99 (c) 97 (d) 95

B. x = the unknown score. (93 + 89 + 96 + 98 + x) ÷ 5 or (376 + x) ÷ 5 = 95 376 + x = 95(5) 376 + x = 475 -376 x= 99

If ab = 10 and a² + b² = 30, solve for y in the equation y = (a+b)². (a) 40 (b) 45 (c) 50 (d) 55

C. First expand the equation (a+b)² or (a+b)(a=b) into y = a² + b² +2ab. You already know ab = 10 and a² + b² = 30, so substitute the known values and solve for y. 30 + 2(10) = 50

Jack loaned Bob $1,500 at an annual interest rate of 7%. After one year, how much will Bob owe Jack? (a) $105 (b) $1,500 (c) $1,605 (d) $1,507

C. First find interest then add to the loan. $1,500 × 0.07 = 106, $106 + $1,500 = 1,605

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) $12.00 (b) $3.50 (c) $42.00 (d) $100.00

C. Multiply 12 miles by $3.50 per mile: 12 × $3.50 = $42.00

The cost of a protein bar increased from $2.50 to $2.80. The percent increase to the $2.80 rate was how much? (a) 16% (b) 10% (c) 15% (d) 12%

D. Find the difference then use that number to divide the original cost $2.50 ÷ $0.30 = 0.12 or 12%

Kevin and Kara are in a pancake-eating contest. Kevin can eat three pancakes per minute, while Kara can eat 3 ½ pancakes per minute. How many total pancakes can they eat in 10 minutes? 52 pancakes 72 pancakes 65 pancakes 44 pancakes

If Kevin eats 3 pancakes in one minute, you know he eats 3(10) = 30 in 10 minutes. If Kara eats 3 ½ per minute, she eats 3.5(10) = 35 in 10 minutes. Add 30 + 35 = 65 and you have your answer.

to get the odds of two events occurring, what do you do?

Multiply the odds, for example

Solve for the following equation: (8 + 2 - 3)(7-9)² A. 28 B. -28 C. 32 D. -32

PEMDAS 8 + 2 - 3 = 7 7 - 9 = -2 (7)(-2)² SOLVE EXPONENT NEXT (-2)²= 4 (7)(4) = 28

A mobile classroom is a rectangular block that is 100 feet by 20 feet in length and width respectively. If a student walks around the block once, how many yards does the student cover?

Perimeter is equal to two times the length added to two times the width, or 2L + 2W. The total distance traveled around the block is the perimeter, which is 2(length) + 2(width). 2(100) + 2(20) = 200 + 40 = 240 feet Set up a proportion to convert feet to yards. 1 yard = 3 feet x yards = 240 feet 1/3 = x/240 240 = 3x x = 80 yards

What is the circumference of a circle?

The distance around a circle circumference = 2πr or π(d)

Rachel is driving to visit her mother, who lives 250 miles away. How long will the drive be, round-trip, if Rachel drives at an average speed of 40 mph?

The distance from Rachel's house to her mother's house is 250 miles, so round-trip, the distance is 500 miles. Plug this into the distance formula: d = rt 500 = 40t 12.5 = t It takes Rachel 12.5 hours to make the round-trip drive. Multiply by 60 to find the answer in minutes. 12.5(60) = 750 minutes

when a question asks you to determine the probability of one or another event occurring, you __ the individual probabilities a)subtract b) add c) multiply d) divide

when a question asks you to determine the probability of one or another event occurring, you add the individual probabilities

How to solve Work problems such as: Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

1/(time for 1st) + 1/(time for 2nd) = 1 / (time for both, or x)

how to SUBTRACT decimals

1. line up the decimals 2. fill in spaces with zeroes (0) 3. bring decimal STRAIGHT DOWN 4. Subtract using correct place value

Changing percents to fractions

-Divide the percent by 100 -Eliminate the percent sign -Reduce if necessary Example: 60% = 60/100 = 3/5

Changing percents to decimals

-Eliminate the percent sign -Move the decimal point two places to the left (sometimes adding zeros will be necessary) Example: 5% = .05

Changing decimals to percents

-Move the decimal point two places to the right -Insert a percent sign Example: .75 = 75%

Which answer is equivalent to seven to the fourth power? a. 0.0007 b. 70,000 c. 1 d. 2401

Seven to the fourth power is 74, which is the equivalent of (7)(7)(7)(7). Multiply to get the answer: 7(7) = 49 49(7) = 343 343(7) = 2401

8 x 7 =

56

mangoes are sold at $8.40 a dozen. How much will 15 mangoes cost? a) 12.60 b) 11.50 c) 10.70 d) 10.50

8.40 MANGOES / 12 TOTAL = .70 EACH MANGO= $.70 X 15 = $10.50

On a 120 question test, a student got 96 correct answers. What percent of the problems did the student work correctly?

96 is what percent of 120?

A carpenter needs to cut four sections, each 3 feet, 8 inches long, from a piece of molding. If the board is only sold by the foot, what's the shortest length of board she can buy? (a) 15 feet (b) 14 feet (c) 16 feet (d) 12 feet

A. Each section is 3²/₃ feet, times that by four and you get 14²/₃ so 15 is the shortest board possible.

Kiya had only one coupon for 10% off one frozen turkey breast. The turkey breast costs $8.50 each, and Kiya wanted to buy two. How much did she pay? (a) $16.15 (b) $17.00 (c) $15.30 (d) $7.65

A. First find the discounted turkey's price ($8.50 × .10 = $0.85, $8.50 - $0.85 = $7.35) then add another $8.50 because she needs two turkey breast. $7.35 + $8.50 = $16.15

For all integers x, which of the following must be true about 4x + 4 a. must be even b. must be odd c. must be a multiple of 3 d. must be a multiple of 5

A. Since x is an integer, multiplying an integer by 4 will result in an even integer. So 4x must be even. Adding 4 to an even value must result in an even number. Therefore 4x + 4 must be even.

Miriam bought five cases of motor oil on sale. A case of motor oil normally costs $24.00, but she was able to purchase the oil for $22.50 a case. How much money did Miriam save on her entire purchase? (a) $7.50 (b) $1.50 (c) $8.00 (d) $22.50

A. Subtract the sale price from the original price, $24.00 − $22.50 = $1.50. Now multiply that number by the amount of cases to get the final answer $1.50 × 5 = $7.50

A carpenter earns $12.30 an hour for a 40-hour week. His overtime pay is 1¹/₂ times his base pay. If he puts in a 46-hour week, how much is his weekly pay? (a) $602.70 (b) $492.00 (c) $565.80 (d) $110.70

A. You need to add the carpenters base pay and overtime to find his total pay for the week. First find his base pay per week: $12.30 × 40hrs = $492. Then find his overtime rate per hour, which is 1¹/₂ time the base pay: $12.30 × 1.5 = $18.45. Multiply this rate by the number of hours of overtime to find his overtime pay: $18.45 × 6 hr. = $110.70. Finally add the base pay and overtime to find the total for the week, $492 + $110.7 = $602.70

what is the area formula for a circle?

A=πr²

In the set of numbers (1, 4, 7, 10, 13, 16, 19, 22, 25) what is the arithmetic mean?

Avoid the temptation to use the formula for finding the arithmetic mean, or average. Instead, notice that each number in the set has the same difference from the previous number so that they form an arithmetic sequence. Whenever that Is true of a set of numbers, the arithmetic mean is equal to the median. Since there are 9 numbers in the set, the 5th number (when all the numbers are in order) is the median. in this case, the 5th number is 13.

Your car uses gasoline at a rate of 21 miles per gallon. If gasoline costs $2.82 per gallon and you drive for 7 hours at a speed of 48 miles per hour, how much will you pay for gasoline for the trip? (a) $38.18 (b) $45.12 (c) $47.73 (d) $59.27

B. First determine the miles traveled d = st (7hr × 48mph = 336 miles), then divide by the rate per gallon, 21. So now you know you need 16 gallons at $2.82 per gallon to pay for the trip. 16 × $2.82 = $45.12

Stan bought a monster truck for a $2,000 down payment and $450 a month for five years. What's the total cost of the monster truck? (a) $4,250 (b) $29,000 (c) $27,000 (d) $34,000

B. Five years contains 60 months, $450 payments at 60 months = $27,000. Now add the down payment, $27,000 + $2,000 = $29,000

The population of Grand Island, Nebraska, grew by 600,000 people between 1995 and 2005, one-fifth more than the town council predicted. The town originally predicted the city;s population to grow by (a) 400,000 (b) 500,000 (c) 300,000 (d) 100,000

B. Let x = the original number predicted. An ¹/₅ would make the population growth ⁶/₅ or 120% of x. Express the equation as 1.2x = 600,000, solve for x. x = 500,000√

Karl is driving in Austria, where the speed limit is posted in kilometers per hour. The car's speedometer shows that he's traveling at a rate of 75 kilometers per hour. Karl knows that a kilometer is about ⁵/₈ of mile. Approximately how many miles per hour is Karl traveling? (a) 47 (b) 120 (c) 50 (d) 53

B. Multiply 75 by ⁵/₈, 375 ÷ 46.8 = 47 mph

A waitress earns an average of 12% of the cost of the food she serves. If she serves $375 worth of food in one evening, how much money in tips will she earn on average? (a) $37 (b) $45 (c) $42 (d) $420

B. Multiply the amount spent on drinks, $375, by 12% (or 0.12) to determine the amount of tips: $375 × 0.12 = $45

Continue the pattern: 6, 9, 13.5, 20.25..., ? a. 32.5 b. 25 c. 30.375 d. 27

The pattern is the previous number multiplied by 1.5. Therefore, 6 × 1.5 = 9; 9 × 1.5 = 13.5; 13.5 × 1.5 = 20.25; and 20.25 × 1.5 = 30.375.

A half-pint of cream is what part of a gallon? (a) ¹/₈ (b) ¹/₄ (c) ¹/₁₆ (d) ¹/₆

C. 2 pints in a quart, 4 quarts to a gallon. Therefore 8 pints are to a gallon or 16 half-pints, ¹/₁₆.

An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m., the plane passes over Sea Side Naval Air Station, 120 miles away. How fast is the aircraft traveling? (a) 400 mph (b) 500 mph (c) 600 mph (d) 700 mph

C. The plane traveled 120 miles in 12 minutes or ¹/₅ of an hour. d=st, 120 = ¹/₅x or 120 × 5 = 600 mph

Alice leaves her house, driving east at 45 miles per hour (mph). Thirty minutes later her husband Dave notices she forgot her cell phone and sets off after her. How fast must Dave travel in order to catch up with Alice 3 hours after he leaves? (a) 49 mph (b) 50.5 mph (c) 52.5 mph (d) 54 mph

C. distance = speed × time. First find how far Alice had traveled 3½ hours at 45 mph, or 157.5 mph. Dave has three hours to cover this distance. Now find his speed. 157.5 mi ÷ 3 hr. = 52.5 mph

If a car travels 1 / 100 of a kilometer each second, how many kilometers does it travel in one hour? a. 36 b. 60 c. 72 d. 100

Find the number of seconds in an hour and then multiply this by the distance the car is traveling each second. 60 seconds in a minutem 60 minutes in an hour 60 x 60 = 3600 seconds in an hour If the car travels 1/100 kilometers in a second, in one hour it will travel 3600 x 1/100 = 36 kilometers

Joe received an hourly wage of $8.15. His boss gave him a 7% raise. How much does Joe make per hour now? (a) $0.57 (b) $8.90 (c) $8.72 (d) $13.85

C.To calculate the new wage first multiply $8.15 × 0.07 = $0.57. Then add that to the original wage, $8.15 + $0.57 = $8.72

Chad's recipe for chocolate chip cookies makes 24 servings of 375 calories each. Chad decided to make 150% of the amount in the recipe rather than the usual 100%. Approximately how many calories are in Chad's batch of cookies?

First, find out how many total calories are in 100% of the recipe: 24(375) = 9,000 calories To find how many calories are in 150% of the recipe, use this equation: x = 9,000 (1.50) x = 13,500

The scale of the model of a car is 1:24. If the full-size car is 12 ft long, how long is the model? a) 4 inches b) 5 inches c) 6 inches d) 7 inches

Convert Ft to inches. 12 inches in every ft, so 12 x 12 = 144 What ratio will give 1:144 reduced to 1:24 x:144 plug and try 6 : 144 = 6√144 = 1:24 C

A bag contains 6 black marbles and 4 white marbles. Sally takes out a black marble and does not put it back. what is the probability that the next marble she picks will also be black? a. 6/10 b. 9/25 c. 1/2 d. 5/9

Count up the total marbles left: 5 black marbles, 4 white marbles Add total to get the denominator 5 + 4 = 9 there are 5 black marbles for numerator = 5/9

On the throw of a six-sided die, what is the probability you that you will roll a number less than 3? a) 1/2 b) 1/6 c) 1/3 d) 2/3

Draw out all the dot options 1 2 3 4 5 6 Each die has a 1/6 odds of rolling The question asks the probability of rolling less than three. There are only two die's less than three: 1 & 2 1/6 + 1/6 = 2/6 = 1/3

A train headed south for Wichita left the station at the same time a train headed north for Des Moines left the same station. The train headed to Wichita traveled 55 miles per hour. The train headed for Des Moines traveled at 70 miles per hour. How many miles apart are the trains at the end of three hours? (a) 210 miles (b) 165 miles (c) 125 miles (d) 375 miles

D. Distance = speed × time, take the distance traveled by the Wichita train (55mph × 3hr = 165 miles) then add that to the distance traveled by the Des Moines train (70mph × 3hr = 210 miles). The trains are 375 miles apart in 3 hours. Another option: add the two trains mph then multiply by 3 hours (55 + 70) = 125 × 3 = 375 miles

If you roll two six-sided dice, what's the probability of not rolling a five on either die? (a) ¹/₃₆ (b) ¹/₆ (c) ⁴/₃₆ (d) ²⁵/₃₆

D. The probability of rolling a 5 is a 1 out of 6 chance, so the probability of NOT rolling a 5 is 5 out of 6. With two die the probability is ⁵/₆ × ⁵/₆ = ²⁵/₃₆

How many square feet of carpeting are needed to carpet a 12-foot × 12-foot room? (a) 24 (b) 120 (c) 48 (d) 144

D. To determine square footage multiply length by width 12 × 12 = 144 sq feet

Barbara worked 30 hours last week. She earned $422. If she was paid $455 this week, approximately how many hours did she work? a) 32 hours b) 35 hours c) 37 hours d) 39 hours

DOLLARS / HOURS first find out the first weeks hourly wage: 422/30 = 14.06 ≈ $14 Then take the second weeks wage and divide by hourly wage 455/14 = ≈$32

What is the prime factorization of 26³ a. 2 x 3 x 13 b. 2 x 2 x 13 x 13 c. 2 x 2 x 3 x 13 x 13 x 13 d. 2 x 2 x 2 x 13 x 13 x 13

Don't calculate or even estimate the value of 26³. The prime factorization of 26 is 2 x 13. So, since there are three factors of 26, there are three factors of 2 and three factors of 13. (2 x 13)³ or 2 x 2 x 2 x 13 x 13 x 13

If |4x - 6| = 18, which of the following is a possible value of x? a. -4 b. -3 c. 4 d. 24

For an equation with an absolute value sign, consider both the positive and the negative values for what is inside the sign. 4x - 6 can equal either 18 or -18. If 4X - 6 = 18 first add 6 to each side, then divide by 4 and x = 6. Since 6 is not an answer choice, try the other equation: 4x - 6 = -18 and add 6 to each side. 4x = -12, divide each side by 4 so that x = -3

If | x - 5 | = 10, what is the smallest possible value of x? a. -15 b. -5 c. 15 d. 25

For an equation with an expression inside the absolute value signs, create two equations: one with a positive value (in this case, 10) and one with a negative value (in this case, -10) Since the question asks for the smallest possible value of x, start with the equation with the negative value. Since x - 5 = -10, add 5 to both sides, and the resulting equation is x = -5

What is 85,000,000,000 in scientific notation? 8.5 x 10^10 8.5 x 10^-10 .85 x 10^11 85 x 10^9

In scientific notation, move the decimal point so it rests after the first number (8). The exponent attached to the 10 expresses the number of decimal points that must be added to the base number (8.5) in order to correctly write the number.

At the arcade, Nick spent 203 tokens on videogames in seven days. Each day he spent five more tokens than the previous day. How many tokens did Nick spend on the third day at the arcade? 14 tokens 24 tokens 29 tokens 34 tokens

Let x = the number of tokens Nick spent on day 1. Set up the following equation and solve for x: x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) + (x + 30) = 203 7x + 105 = 203 x = 14 tokens We know Nick spent 14 tokens on the first day. To find what he spent on the third day, add 10 tokens to get 24 tokens

A full 10 liter container of diluted orange juice contains 20% water and 80% pure juice. After half of the diluted orange juice is consumed, 1 liter of pure juice is added to sweeten the taste. What is the ratio of liters of water to liters of pure juice after the liter of pure juice is added? a. 1:5 b. 1:4 c. 4:5 d. 1:1

Since half of the 10 liters of diluted juice are consumed, there must be only 5 liters remaining. 20% is water and 80% is pure juice, so there is now 1 liter of water and 4 liters of pure juice. Another liter of pure juice is added, so there is 5 liters of pure juice. The ratio is 1:5.

Michael can wash a car in two hours, and Jim can wash the same car in four hours. How long will it take the two of them working together to wash two of the same cars?

Since the problem states how long it takes each person to wash the car, the units of which are Hours/Car, take the reciprocal of the times to get the rates in terms of cars/hour and add them together to the combined rate: 1/2 + 1/4 = 2 (Cars) / x (time) 2/4 + 1/4 = 3/4 cars/hour working together. invert that combined rate to determine that they can wash 1 car in 4/3 hour. however, the question asks how long it will take to wash two cars, so that would be 8/3 = 2 2/3 hours

A building has 2/5 of its floors below ground. What is the ratio of the # of floors above ground to the # below ground? a. 5:2 b. 3:2 c. 2:3 d. 2:5

The question provides a part to whole ratio and asks for a part to part ratio. If 2 of the 5 floors are above ground, then 5-2 = 3 floors must be below ground. So the ratio of floors below ground to floors above ground is 3:2

What is the arithmetic mean?

The same as mean (and average.)

Will is filling up his pool for the summer, and water from the hose flows into the pool at 6 gallons per minute. The pool holds 17,280 gallons. How long, in hours, does it take to fill the pool?

The water is flowing into the pool at a rate of 6 gallons per minute. Do the math to see how long it takes to get to 17,280 gallons: 17,280 gallons ÷ 6 gallons/minute = 2,880 minutes To convert to hours, divide by 60 minutes: 2,880 minutes ÷ 60 minutes/hour = 48 hours

How many ways are there to choose an outfit from 3 shirts and 4 pairs of pants, assuming an outfit consists of one shirt and one pair of pants? a. 4 b. 7 c. 12 d. 20

To find the number of possible combinations consisting of two different elements, multiply how much of each element you have. Since each outfit consists of one shirt and one pair of pants, take the number of shirts (3) and the number of pairs of pants (4), and multiply them together. 3 x 4 = 12

Terri has a jar of orange, blue, green, and red chocolate candies. In the jar are 75 orange candies, 62 blue candies, and 52 green candies. If there is a total of 252 candies in the jar, what is the probability that Terri will pick a red candy?

To solve this problem, first find the number of red candies in the jar by adding the numbers of all the other candies together, then subtracting from the total. 75 orange + 62 blue + 52 green = 189 candies 252 - 189 = 63 red candies Probability is the chance that a certain event will happen. Since there are 63 red candies out of a total of 250 candies, divide 63 by 252. Reduce the fraction by dividing the numerator and denominator by 63. 63/252 ÷ 63/63 = ¼

Express 6/4 as a percentage. A. 0.5% B. 150% C. 50% D. 500%

divide 6 by 4 in decimal format and multiply by 100 6√4 = 1.5 x 100 = 150%

Math translations for: is of a number what percent what number

is = of x (multiply) a number n (variable) what percent n (variable) what number n (variable)

whenever there is a true set or pattern of numbers, the arithmetic mean is equal to the __

median. For example: Since there are nine numbers in this set, the 5th number is the median, or 13. (1, 4, 7, 10, 13, 16, 19, 22, 25)

In the past year, XYZ corporation reported sales of $1.17 of 10^6. The year before, the company's sales were $9.00 x 10^5. What was the percentage change in sales? a) 30% decrease b) 27% increase c) 27% decrease d) 30% increase

must make the same base to subtract