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Basic Math

Basic Math Practice Test: Practice Test 5

Practice Test 5 for Basic Math: real questions and explanations from the Varsity Tutors practice-test pool.

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Question 1

Solve:

  1. (correct answer)

Explanation: Use order of operations, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to solve. Since there are no parentheses or exponents we can go straight to multiplication and division. and Therefore the following happens: Then add and subtract.

Question 2

In March, an athlete weighed pounds. In April, the same athlete weighed pounds. What is the athlete's percentage of weight loss?

  1. (correct answer)

Explanation: The formula to find percentage change is . So for our athlete, our new weight is 170 pounds, and the original weight is 195 pounds. Because the question already tells us that we need to find the percent lost, or percent decrease, we can drop the negative sign in the answer.

Question 3

If I want yards of fabric, how many inches will I have?

  1. inches (correct answer)
  2. inches
  3. inches
  4. inches

Explanation: 1. Find out how many feet you have: Knowing that there are 3 feet in a yard, you have 3 x 4 yards = 12 feet of fabric. 2. Find out how many inches you have: Knowing that there are 12 inches in a foot, you have 12 x 12 inches=144 inches of fabric.

Question 4

John recently bought the following school supplies: a calculator for , a pencil bag for , a mechanical pencil for , and a set of pens for .

How much did John spend in total on school supplies?

  1. (correct answer)

Explanation: In order to solve this problem, you must add all of the costs of school supplies together. This can be done through the following equation: Therefore, the total amount that John spent on school supplies is .

Question 5

Kevin has won toys from a competition and decides to keep toys for himself. He would like to give the rest of the toys to four of his close friends.

If each of Kevin's friends receive the same number of toys from Kevin, how many will be remaining?

  1. (correct answer)

Explanation: The correct answer is 2 remaining toys. Kevin has 34 toys to start and he keeps 4 for himself. This means that he has 30 toys to give to four friends. When we divide 30 by 4, we get 7.5. Since each friend cannot get half a toy, each friend can receive 7 toys. This means that of the 30 toys, there will be 2 toys remaining.

Question 6

Change to a decimal.

  1. (correct answer)

Explanation: To change a percent to a decimal, drop the "%" sign then divide by 100.

Question 7

Convert to a percentage.

  1. (correct answer)

Explanation: The correct answer is 20%. This can be obtained by first converting the fraction to a decimal and then multiplying by 100 to get a percentage.

Question 8

Determine the answer as an improper fraction:

  1. (correct answer)

Explanation: 1. Invert the second fraction: 2. Multiply the two fractions: 3. Reduce the improper fraction: So the improper fraction can be reduced to .

Question 9

What is of ?

  1. (correct answer)

Explanation: Before multiplying, it's necessary to convert 0.25% to a decimal, which is 0.0025. Multiply this 0.0025, with 100. The correct answer is 0.25.

Question 10

Solve the following:

  1. (correct answer)

Explanation: The correct answer is and can be found by using reciprocals as shown below: The first step is to identify that 4 can be written as 4 divided by 1. You can then take the first fraction and multiple it by the reciprocal of the second fraction, which can be found by switching the numerator and denominator. From there, you solve and simplify until you get to the final answer.

Question 11

Change to a percent.

  1. (correct answer)

Explanation: To convert a fraction into a percent, we need to first change the fraction into a decimal. Now, change the decimal into a percent by multiplying by 100 and adding a percent sign. Add a percent sign

Question 12

Karen plays on her school's basketball team. She keeps track of the number of points she scores in each game. For the past 6 games, she scored 23 points, 10 points, 34 points, 9 points, 12 points, and 11 points. What is the range for the number of points she scored over the past 6 games?

  1. (correct answer)

Explanation: To find the range, place the numbers in numerical order: Then, subtract the smallest value from the largest value.

Question 13

Baseballs can only be bought in packages of . If team needs balls for the season and always rounds that estimate up, how many packages do they need?

  1. (correct answer)

Explanation: 1. Round 145 to the nearest 10: Since there is a 5 in the ones place, 145 rounds up to 150. 2. Divide the rounded number of baseballs by 10 since they come in packages of 10: 150/10=15 packages

Question 14

What is as a percent?

  1. (correct answer)

Explanation: To change a demical to a percent, multiply the decimal by 100 and then add the percent sign. Add the percent sign.

Question 15

What is expressed as a percentage rounded to the nearest hundredth?

  1. (correct answer)

Explanation: Percents are numbers expressing parts of : is the same thing as saying parts of or The simplest way to convert a decimal to a percentage is to move the decimal place over two places to the right. We move the decimal point to after the hundredths place because we are rewriting the decimal as a portion of . Therefore: In everyday usage, percents usually are between and . However, when a number is greater than , it's corresponding percentage is going to be greater than . The next step of this problem is to round the percentage we have to the nearest hundredth. The number in the thousandths place is , therefore, we're going to round up: is therefore our final answer.

Question 16

Jane bought a pencil for , a skirt for , a coat for , and a headband for . How much did Jane pay in total for all the items she bought?

  1. (correct answer)

Explanation: Add up all the individual items. Add

Question 17

In 2012, a university received 150,249 applicants. In 2013, the same university received 190,201 applicants. By what percent did the total number of applicants increase from 2012 to 2013?

  1. (correct answer)

Explanation: To find the percent change, use the following formula: Our new number of applicants is 190,201, while the original number of applicants is 150,249.

Question 18

If I want yards of fabric, how many inches will I have?

  1. inches (correct answer)
  2. inches
  3. inches
  4. inches

Explanation: 1. Find out how many feet you have: Knowing that there are 3 feet in a yard, you have 3 x 4 yards = 12 feet of fabric. 2. Find out how many inches you have: Knowing that there are 12 inches in a foot, you have 12 x 12 inches=144 inches of fabric.

Question 19

Solve for .

  1. (correct answer)

Explanation: Add both sides by 9 to isolate the x on one side. Multiply both sides by 5. Divide boths ides b 9.

Question 20

Find the value of in the ratio table above.

  1. (correct answer)

Explanation: To find , we can set up the following ratios: Now, cross-multiply and solve.

Question 21

Find the sum.

  1. (correct answer)

Explanation: To add mixed numbers, you need to first change both of them into improper fractions. Then, add the two improper fractions like you would any other fraction. We need both fractions to have the same denominator before we can add them. Since 27 is a multiple of 3, we only need to change 1 fraction. Now, we can add these fractions. Finally, change the improper fraction back into a mixed number.

Question 22

Jimmy started taking his math test at 11:03AM, and he finished at 12:29PM. How many minutes did it take Jimmy to finish the test?

  1. (correct answer)

Explanation: First, we need to find how long it took Jimmy to finish the test. Subtract the hours, then subtract the minutes. Now, the question asks how many MINUTES it takes Jimmy to finish the test. Convert the hour into minutes.

Question 23

Solve for .

  1. (correct answer)

Explanation: Start by isolating the term with to one side. Add 10 on both sides. Divide both sides by 7.

Question 24

If painters can paint houses in day, how many painters would it take to paint houses in day?

  1. (correct answer)

Explanation: We can set up the following proportions using the given information: Now, cross multiply these two fractions to get the following equation: Divide both sides by .

Question 25

What is of ?

  1. (correct answer)

Explanation: Before multiplying, it's necessary to convert 0.25% to a decimal, which is 0.0025. Multiply this 0.0025, with 100. The correct answer is 0.25.