# ASVAB Arithmetic Reasoning Test 2

#### Mike made a snack mix by combining 1 pound of nuts that cost $13.50 per pound; 2 pounds of pretzels that cost $4.25 per pound; and 4 pounds of cheese crackers that cost $4.60 per pound. What is the price per pound of Mike’s snack mix?

Set up the following equation and solve for x: 13.50(1) + 4.25(2) + 4.60(4) = x(1 + 2 + 4) 13.50 + 8.50 + 18.40 = 7x x = 5.7714 Mike's snack mix costs about $5.77 per pound.

#### 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?

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.

#### Ellie wants to give her granddaughter a present of $500 saved in a bank account. If Ellie puts $350 in the account which earns an 8% annual interest rate, how long must she wait before the account is worth $500?

The interest amount is $150, which is the difference between the desired amount and what Ellie originally deposits. You can use the interest formula: I = Prt, where I is interest, P is principal, r is rate, and t is time. Just plug in I = 150, P = 350, and r = 0.08, and solve for t: 150 = 350(0.08)t 28t = 150 t = 5.36 years, or approximately 5 years 4 months.

#### 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

#### Continue the pattern: 6, 9, 13.5, 20.25, ?

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.

#### What should come next in the following sequence? 64a, 55b, 46c, 37d, 28e, ?

The pattern is descending increments of 9 followed by the first letter, second letter, third letter, and so on.

#### 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?

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 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

#### Edward is scheduled to detail 23 cars this week. If he details 3 cars on Monday, how many must he detail each remaining day on average to finish by the end of the day on Saturday?

First, subtract the cars Edward detailed on Monday. 23 - 3 = 20 Edward has Tuesday, Wednesday, Thursday, Friday, and Saturday left to work, so he has a total of 5 days left. Divide 20 by 5 to find how many cars he must detail each day. 20/5 = 4 cars each day

#### 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

#### 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?

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.

#### 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.

#### What is the result when 7 is added to the product of 2 and 3?

To get your desired answer of 2(3) + 7 = 13 you will need to find out which mathematical operation you should perform first. Use the acronym PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) to determine the order of operations. In this problem, perform the multiplication operation first, followed by addition.

#### Which of the following is equivalent to 2 times the total of x plus y?

2 times the total of x plus y is 2(x + y). From there, use the Distributive Property to multiply the 2 by each term inside the parenthesis. 2(x + y) = 2x + 2y

#### The absolute value of 5 plus a number equals 10. Which of the following options is the correct solution set for the above equation?

The absolute value of 5 plus a number equals 10” should be written as |5 + x| = 10. Absolute value means the distance of a number from zero, so whenever you solve for the number inside absolute value bars, you must consider both the positive and negative values. Take away the bars and set the expression equal to both 10 and -10. 5 + x = 10 gives you x = 5, and 5 + x = -10 gives you x = -15. The solution set is x = {-15, 5}.

#### What is the absolute value of the quantity two minus seven?

The absolute value of the quantity two minus seven” should be written as |2 - 7|. Absolute value is the distance of a number from zero, and since distances cannot be negative, absolute values are always positive numbers. To take the absolute value, simplify the expression between the absolute value bars and then take the positive value of it. |2 – 7| = |-5| = 5.

#### Which of the following numbers is divisible by 3?

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. 8 + 5 + 0 + 1 + 9 + 4 + 5 + 7 = 39 39 divided by 3 is 13 with no remainders, so the number is divisible by 3.

#### Which of the following is true?

It is true that if a number is divisible by both 2 and 3, it is also divisible by 6. For example, 108 is divisible by 2 (108 ÷ 2 = 54) and by 3 (1 + 0 + 8 = 9 ÷ 3 = 3), and therefore is also divisible by 6.