*THIS ONE* ASVAB 2020 Arithmetic Reasoning

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

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%

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

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

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

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)

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

12 x 12

144

how many feet are in a yard?

3 feet

7 x 6

42

12 x 4 =

48

8 x 6

48

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

8 x 7 =

56

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

8 x 8 =

64

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 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.

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.

formula for area of a rectangle

A=lw

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.

Formula for circumference of a circle

C = 2πr or C = πd

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 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 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

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

how to solve long division

DONT FORGET TO CARRY DOWN THE NUMBER BEFORE ATTEMPTING TO SOLVE

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

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

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 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

What is prime factorization?

Finding all the prime factors

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

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

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

INCREASED AMOUNT / ORIGINAL AMOUNT = N / 100

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

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

Multiply the odds, for example

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)

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 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

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

What is the circumference of a circle?

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

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

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.)

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

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!

HOW TO SOLVE UNIT RATIO PROBLEMS

UNIT (AMOUNT) / TOTAL GIVEN

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

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

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

What are absolute values?

distance from zero. An absolute value cannot be negative, even if the number is negative. the absolute values of both 7 and −7 are equal to 7, because they are both the same distance from 0. Absolute value is symbolized with two vertical lines, | |. |5| = 5

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%

What is a radius?

half the diameter

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)

volume of a rectangle =

length x width x height

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)

How to set up miles, gas gallon problems?

miles ------ gallons miles/gallons

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

what is the rule for -2 x -2

negative x negative = postive

distance =

rate x time d= rt

How to set up division of 10.47 / 87.67

top goes in the house Numerator divided by the denominator

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