6th Grade Math: Hardest Practice Exam! Trivia Quiz

1. A certain map uses a scale of 1 inch equals 25 miles. How many miles are represented by 5 inches on this map?

25

125

150

160

To determine the number of miles represented by 5 inches on the map, you can use the given scale of 1 inch equals 25 miles. Multiply the length on the map (in inches) by the scale factor to find the corresponding distance in miles. Distance in miles = Length on the map × Scale factor Distance in miles = 5 inches × 25 miles/inch Distance in miles = 125 miles. So, 5 inches on the map represents 125 miles in reality.

Explanation

To determine the number of miles represented by 5 inches on the map, you can use the given scale of 1 inch equals 25 miles. Multiply the length on the map (in inches) by the scale factor to find the corresponding distance in miles. Distance in miles = Length on the map × Scale factor Distance in miles = 5 inches × 25 miles/inch Distance in miles = 125 miles. So, 5 inches on the map represents 125 miles in reality.

2. If a freight train travels at a speed of 20 miles per hour for 6 hours, how far will it travel?

120 miles

80 miles

26 miles

140 miles

Distance = Speed × Time

Distance = 20 miles/hour × 6 hours = 120 miles

So, the freight train will travel a distance of 120 miles.

Explanation

Distance = Speed × Time

Distance = 20 miles/hour × 6 hours = 120 miles

So, the freight train will travel a distance of 120 miles.

3. If x − 3=6, what is the value of x?

2

3

9

6

Explanation

4. Sheila has been given 5 minutes to solve 20 arithmetic problems. What is the minimum rate Sheila can work in order to finish in time?

1 problems per minute

2 problems per minute

4 problems per minute

6 problems per minute

To find the minimum rate at which Sheila needs to work to finish solving 20 arithmetic problems in 5 minutes, we can calculate the number of problems she needs to solve per minute.

Minimum rate = Number of problems / Time available

Minimum rate = 20 problems / 5 minutes = 4 problems/minute

Explanation

To find the minimum rate at which Sheila needs to work to finish solving 20 arithmetic problems in 5 minutes, we can calculate the number of problems she needs to solve per minute.

Minimum rate = Number of problems / Time available

Minimum rate = 20 problems / 5 minutes = 4 problems/minute

5. What is 60%of 30?

1.8

18

180

16

To find 60% of 30, you multiply 30 by 0.60 (which is the decimal equivalent of 60%).

60% of 30 = 0.60 * 30 = 18

So, 60% of 30 is 18.

Explanation

To find 60% of 30, you multiply 30 by 0.60 (which is the decimal equivalent of 60%).

60% of 30 = 0.60 * 30 = 18

So, 60% of 30 is 18.

6. What is the value of 7/9 * 2/9?

9/81

14/81

9/9

11/81

To multiply fractions, you simply multiply the numerators (top numbers) together to get the new numerator and multiply the denominators (bottom numbers) together to get the new denominator.

So, 7/9×2/9=14/81

Explanation

To multiply fractions, you simply multiply the numerators (top numbers) together to get the new numerator and multiply the denominators (bottom numbers) together to get the new denominator.

So, 7/9×2/9=14/81

7. The weekly milk order for the Tranquility Inn includes 40 gallons of low-fat milk and 15 gallons of chocolate milk. What is the ratio of the number of low-fat gallons to chocolate gallons in the Tranquility Inn's weekly milk order?

5:1

8:3

6:3

7:4

The ratio of low-fat milk gallons to chocolate milk gallons in the Tranquility Inn's weekly order is 40:15, which simplifies to 8:3. To simplify the ratio, you can find the greatest common divisor (GCD) of both numbers (40 and 15), which is 5. Divide both numbers by the GCD: 40 ÷ 5 = 8, 15 ÷ 5 = 3. Hence, the correct option is B.

Explanation

The ratio of low-fat milk gallons to chocolate milk gallons in the Tranquility Inn's weekly order is 40:15, which simplifies to 8:3. To simplify the ratio, you can find the greatest common divisor (GCD) of both numbers (40 and 15), which is 5. Divide both numbers by the GCD: 40 ÷ 5 = 8, 15 ÷ 5 = 3. Hence, the correct option is B.

8. A company makes 5 blue cars for every 3 white cars it makes. If the company makes 15 white cars in one day, how many blue cars will it make?

9

13

25

30

Let's set up a proportion using the given ratio and the number of white cars: Blue Cars / White Cars = 5 / 3

We want to find the number of blue cars when there are 15 white cars: Blue Cars / 15 = 5 / 3

Now, cross-multiply and solve for Blue Cars: Blue Cars = (5 / 3) * 15 Blue Cars = 25

Explanation

Let's set up a proportion using the given ratio and the number of white cars: Blue Cars / White Cars = 5 / 3

We want to find the number of blue cars when there are 15 white cars: Blue Cars / 15 = 5 / 3

Now, cross-multiply and solve for Blue Cars: Blue Cars = (5 / 3) * 15 Blue Cars = 25

9. What value of k makes the following equation true? k ÷3=36

108

98

38

81

To find the value of k that makes the equation k / 3 = 36 true, you need to solve for k.

Given: k /3 = 36

Multiply both sides of the equation by 3 to isolate k: k = 36×3 = 108

Explanation

To find the value of k that makes the equation k / 3 = 36 true, you need to solve for k.

Given: k /3 = 36

Multiply both sides of the equation by 3 to isolate k: k = 36×3 = 108

10. What is 12/60 expressed in lowest terms?

1/8

1/6

1/5

4/5

Explanation

11. When wheel B turns 2 revolutions, wheel A turns 5 revolutions. When wheel A turns 40 revolutions, how many revolutions does wheel B turn?

4

16

80

84

Let's create a ratio: Revolutions of A / Revolutions of B = 5 / 2

Now we want to find out how many revolutions wheel B will turn when wheel A turns 40 revolutions using the same ratio.

We know that Revolutions of A = 40. Let's solve for Revolutions of B: 40 / Revolutions of B = 5 / 2

Now, cross-multiply and solve for Revolutions of B:

2 * 40 = 5 * Revolutions of B

80 / 5 = Revolutions of B = 16

Explanation

Let's create a ratio: Revolutions of A / Revolutions of B = 5 / 2

Now we want to find out how many revolutions wheel B will turn when wheel A turns 40 revolutions using the same ratio.

We know that Revolutions of A = 40. Let's solve for Revolutions of B: 40 / Revolutions of B = 5 / 2

Now, cross-multiply and solve for Revolutions of B:

2 * 40 = 5 * Revolutions of B

80 / 5 = Revolutions of B = 16

12. If 50% of a number is 20, what is 75% of the number?

8

15

30

40

Let's call the number "x."

We can set up an equation using the information provided: 0.5 * x = 20

Now, solve for x: x = 20 / 0.5 x = 40

So, the number is 40.

To find 75% of the number: 75% of 40 = 0.75 * 40 = 30

Therefore, 75% of the number is 30.

Explanation

Let's call the number "x."

We can set up an equation using the information provided: 0.5 * x = 20

Now, solve for x: x = 20 / 0.5 x = 40

So, the number is 40.

To find 75% of the number: 75% of 40 = 0.75 * 40 = 30

Therefore, 75% of the number is 30.

13. What is the value of 12 divided by -3?

9

4

-4

2

When dividing a positive number by a negative number, the result is always negative. In this case, 12 divided by -3 would result in -4.

Explanation

When dividing a positive number by a negative number, the result is always negative. In this case, 12 divided by -3 would result in -4.

14. What is the order of the following set of numbers from greatest to least? 1 1/3, 2/3, -1/3, 9/3

-1/3, 1 1/3, 2/3, 9/3

9/3, 1 1/3, 2/3, -1/3

-1/3, 9/3, 1 1/3, 2/3

1 1/3, 2/3, -1/3, 9/3

To order the set of numbers from greatest to least, we'll need to compare their values:

9/3 (3): This is the largest number in the set, as 9/5 is equal to 1.8.

1 1/3 ( i.e. 4/3) (1.333...): After that comes 1 1/3, which is approximately 1.333....

2/3 (0.666...): The next largest number is 2/3, which is approximately 0.666....

-1/3 (-0.333...): Finally, the smallest number in the set is -1/3, which is approximately -0.333....

Only comparing numerators with the common denominator 3 for all fractions, we can also infer the answer directly. 9/3 > 4/3 > 2/3 > -1/3.

Hence, option B is correct.

Explanation

To order the set of numbers from greatest to least, we'll need to compare their values:

9/3 (3): This is the largest number in the set, as 9/5 is equal to 1.8.

1 1/3 ( i.e. 4/3) (1.333...): After that comes 1 1/3, which is approximately 1.333....

2/3 (0.666...): The next largest number is 2/3, which is approximately 0.666....

-1/3 (-0.333...): Finally, the smallest number in the set is -1/3, which is approximately -0.333....

Only comparing numerators with the common denominator 3 for all fractions, we can also infer the answer directly. 9/3 > 4/3 > 2/3 > -1/3.

Hence, option B is correct.

15. The ticket prices to a play are $5.00 for teachers and $3.00 for students. How much will it cost for a group of 71 students and 5 teachers to see the play?

$228.00

$238.00

$370.00

$240.00

To calculate the total cost for a group of 71 students and 5 teachers to see the play, you need to multiply the number of students by the student ticket price and the number of teachers by the teacher ticket price, then add the two amounts together.

Total cost = (Number of students × Student ticket price) + (Number of teachers × Teacher ticket price)

Total cost = (71 students × $3.00/student) + (5 teachers × $5.00/teacher)

Total cost = $213.00 + $25.00 = $238.00

So, it will cost a group of 71 students and 5 teachers $238.00 to see the play.

Explanation

To calculate the total cost for a group of 71 students and 5 teachers to see the play, you need to multiply the number of students by the student ticket price and the number of teachers by the teacher ticket price, then add the two amounts together.

Total cost = (Number of students × Student ticket price) + (Number of teachers × Teacher ticket price)

Total cost = (71 students × $3.00/student) + (5 teachers × $5.00/teacher)

Total cost = $213.00 + $25.00 = $238.00

So, it will cost a group of 71 students and 5 teachers $238.00 to see the play.

16. What is the greatest common divisor of 54, 36, and 24?

2

3

6

10

To find the greatest common divisor (GCD) of 54, 36, and 24, you can use various methods, such as prime factorization or the "division ladder" approach. Let's use the prime factorization method:

Prime factorization of 54: 54 = 2 × 3 × 3 × 3

Prime factorization of 36: 36 = 2 × 2 × 3 × 3

Prime factorization of 24: 24 = 2 × 2 × 2 × 3

Now, look for the common factors among these prime factorizations:

Common factors of 54, 36, and 24: 2^1 and 3^1

The GCD is the product of the common prime factors raised to the lowest exponent they appear in:

GCD = 2^1 × 3^1 = 2 × 3 = 6

Explanation

To find the greatest common divisor (GCD) of 54, 36, and 24, you can use various methods, such as prime factorization or the "division ladder" approach. Let's use the prime factorization method:

Prime factorization of 54: 54 = 2 × 3 × 3 × 3

Prime factorization of 36: 36 = 2 × 2 × 3 × 3

Prime factorization of 24: 24 = 2 × 2 × 2 × 3

Now, look for the common factors among these prime factorizations:

Common factors of 54, 36, and 24: 2^1 and 3^1

The GCD is the product of the common prime factors raised to the lowest exponent they appear in:

GCD = 2^1 × 3^1 = 2 × 3 = 6

17. A soccer team has $90.00 to buy soccer balls. If one soccer ball costs $15.60, what is the greatest number of soccer balls the team can buy?

4

5

6

2

To find the greatest number of soccer balls the team can buy, you need to divide the total amount they have ($90.00) by the cost of one soccer ball ($15.60).

Number of soccer balls = Total amount available / Cost of one soccer ball

Number of soccer balls = $90.00 / $15.60

Number of soccer balls ≈ 5.7692

Since you can't have a fraction of a soccer ball, you'll round down to the nearest whole number.

The team can buy a maximum of 5 soccer balls with $90.00.

Explanation

To find the greatest number of soccer balls the team can buy, you need to divide the total amount they have ($90.00) by the cost of one soccer ball ($15.60).

Number of soccer balls = Total amount available / Cost of one soccer ball

Number of soccer balls = $90.00 / $15.60

Number of soccer balls ≈ 5.7692

Since you can't have a fraction of a soccer ball, you'll round down to the nearest whole number.

The team can buy a maximum of 5 soccer balls with $90.00.

18. It takes a machine 12 minutes to fill 200 bottles of soda. At this rate, how many minutes will it take the machine to fill 500 bottles of soda?

25 minutes

28 minutes

30 minutes

40 minutes

To solve this problem, you can set up a proportion based on the rate of filling bottles.

Let's set up the proportion: Time / Number of bottles = Constant rate

For the first scenario: 12 minutes / 200 bottles = Constant rate

Now, we can use the same constant rate for the second scenario to find the time needed to fill 500 bottles: Time / 500 bottles = Constant rate

Solve for Time: Time = 500 bottles × Constant rate

Substitute the constant rate from the first scenario (12 minutes / 200 bottles): Time = 500 bottles × (12 minutes / 200 bottles)

Now, perform the calculation: Time = (500 × 12) / 200

Time = 6000 / 200 Time = 30

Explanation

To solve this problem, you can set up a proportion based on the rate of filling bottles.

Let's set up the proportion: Time / Number of bottles = Constant rate

For the first scenario: 12 minutes / 200 bottles = Constant rate

Now, we can use the same constant rate for the second scenario to find the time needed to fill 500 bottles: Time / 500 bottles = Constant rate

Solve for Time: Time = 500 bottles × Constant rate

Substitute the constant rate from the first scenario (12 minutes / 200 bottles): Time = 500 bottles × (12 minutes / 200 bottles)

Now, perform the calculation: Time = (500 × 12) / 200

Time = 6000 / 200 Time = 30

19. One morning, the temperature was 5° below zero. By noon, the temperature rose 20° Fahrenheit (F) and then dropped 8°F by evening. What was the evening temperature?

17* below zero

15* below zero

7* above zero

14* below zero

Let's break down the temperature changes step by step:

Morning temperature: -5°F (5 degrees below zero)

Temperature at noon: -5°F + 20°F = 15°F

Temperature in the evening: 15°F - 8°F = 7°F

So, the evening temperature was 7°F (7 degrees above zero)

Explanation

Let's break down the temperature changes step by step:

Morning temperature: -5°F (5 degrees below zero)

Temperature at noon: -5°F + 20°F = 15°F

Temperature in the evening: 15°F - 8°F = 7°F

So, the evening temperature was 7°F (7 degrees above zero)

20. The original price of a new bicycle is $138.00. If the bicycle is marked down 15%, what is the new price?

$20.17

$117.30

$123.00

$115.30

To find the new price after a markdown, you need to calculate 85% of the original price (since the price is marked down by 15%).

Calculate the markdown amount: Markdown amount = Original price × Markdown percentage

Markdown amount = $138.00 × 0.15 = $20.70

Now, subtract the markdown amount from the original price to find the new price: New price = Original price - Markdown amount

New price = $138.00 - $20.70 = $117.30

So, after a 15% markdown, the new price of the bicycle is $117.30.

Explanation

To find the new price after a markdown, you need to calculate 85% of the original price (since the price is marked down by 15%).

Calculate the markdown amount: Markdown amount = Original price × Markdown percentage

Markdown amount = $138.00 × 0.15 = $20.70

Now, subtract the markdown amount from the original price to find the new price: New price = Original price - Markdown amount

New price = $138.00 - $20.70 = $117.30

So, after a 15% markdown, the new price of the bicycle is $117.30.

21. Marcus spent $3.25 to wash his car. If one quarter operates the car wash for 60 seconds, how long did it take him to wash his car?

10 minutes

13 minutes

16 minutes

15 minutes

To find out how long it took Marcus to wash his car, we can calculate the number of quarters he used and then convert that to seconds.

Cost per quarter = $0.25

Number of quarters used = Cost to wash the car / Cost per quarter

Number of quarters used = $3.25 / $0.25 = 13

Now, multiply the number of quarters by the time operated per quarter: Time taken = Number of quarters used × Time per quarter

Time taken = 13 quarters × 60 seconds/quarter = 780 seconds / 60 = 13 minutes

Explanation

To find out how long it took Marcus to wash his car, we can calculate the number of quarters he used and then convert that to seconds.

Cost per quarter = $0.25

Number of quarters used = Cost to wash the car / Cost per quarter

Number of quarters used = $3.25 / $0.25 = 13

Now, multiply the number of quarters by the time operated per quarter: Time taken = Number of quarters used × Time per quarter

Time taken = 13 quarters × 60 seconds/quarter = 780 seconds / 60 = 13 minutes

22. What is the value of 10/11 * 11/12?

5/6

21/23

2

5

When multiplying fractions, we multiply the numerators together and the denominators together. In this case, multiplying 10/11 by 11/12 gives us (10 * 11) / (11 * 12), which simplifies to 110/132. To simplify further, we can divide both the numerator and denominator by their greatest common divisor, which is 22. Dividing 110 by 22 gives us 5, and dividing 132 by 22 gives us 6. Therefore, the simplified value of 10/11 * 11/12 is 5/6.

Explanation

When multiplying fractions, we multiply the numerators together and the denominators together. In this case, multiplying 10/11 by 11/12 gives us (10 * 11) / (11 * 12), which simplifies to 110/132. To simplify further, we can divide both the numerator and denominator by their greatest common divisor, which is 22. Dividing 110 by 22 gives us 5, and dividing 132 by 22 gives us 6. Therefore, the simplified value of 10/11 * 11/12 is 5/6.

23. How many inches are in 2 1/2 feet?

24

25

30

35

There are 12 inches in a foot. To convert feet to inches, you can multiply the number of feet by 12.

Given: 2 feet and 1/2 (or 0.5) feet

Convert 2 feet to inches: 2 feet × 12 inches/foot = 24 inches

Convert 0.5 feet to inches: 0.5 feet × 12 inches/foot = 6 inches

Now, add the inches together: 24 inches + 6 inches = 30 inches

Explanation

There are 12 inches in a foot. To convert feet to inches, you can multiply the number of feet by 12.

Given: 2 feet and 1/2 (or 0.5) feet

Convert 2 feet to inches: 2 feet × 12 inches/foot = 24 inches

Convert 0.5 feet to inches: 0.5 feet × 12 inches/foot = 6 inches

Now, add the inches together: 24 inches + 6 inches = 30 inches

24. The vice president of sales took a client out to lunch. If the lunch was $44 and she gave a 20% tip, how much money did she spend on lunch?

$8.80

$35.20

$52.80

$60.80

First, calculate the tip amount: Tip = (Tip percentage / 100) * Cost of lunch Tip = (20 / 100) * $44 Tip = $8.80

Now, add the tip to the cost of the lunch to find the total amount spent: Total amount spent = Cost of lunch + Tip Total amount spent = $44 + $8.80 Total amount spent = $52.80

Explanation

First, calculate the tip amount: Tip = (Tip percentage / 100) * Cost of lunch Tip = (20 / 100) * $44 Tip = $8.80

Now, add the tip to the cost of the lunch to find the total amount spent: Total amount spent = Cost of lunch + Tip Total amount spent = $44 + $8.80 Total amount spent = $52.80

25. A survey of 1000 registered voters revealed that 450 people would vote for candidate A in an upcoming election. If 220,000 people vote in the election, how many votes would the survey takers predict candidate A should receive?

44,500

48,900

99,000

91,000

Let's set up a proportion using the surveyed votes and the total votes: Votes for candidate A (surveyed) / Total surveyed voters = Votes for candidate A (predicted) / Total number of people voting

Votes for candidate A (predicted) / 220,000 = 450 / 1000

Votes for candidate A (predicted) = 450 * 220 = 99,000

Explanation

Let's set up a proportion using the surveyed votes and the total votes: Votes for candidate A (surveyed) / Total surveyed voters = Votes for candidate A (predicted) / Total number of people voting

Votes for candidate A (predicted) / 220,000 = 450 / 1000

Votes for candidate A (predicted) = 450 * 220 = 99,000

26. A farmer harvested 14,000 pounds of almonds from an 8-acre orchard. Which proportion could be solved to find x, the expected harvest from a 30-acre orchard?

8/14,000=x/30

8/14,000=30/x

30/14,000=x/8

20/14,000=x/8

Let's set up the ratio of harvest to orchard size: Harvest / Orchard size = 14,000 pounds / 8 acres

Now, let's use the same ratio to find the expected harvest from a 30-acre orchard: Expected harvest / Orchard size = x pounds / 30 acres.

We can set up a proportion using the ratios: (14,000 pounds / 8 acres) = (x pounds / 30 acres) which can also be written as 8 / 14,000 = 30 / x.

Hence option B is correct.

Explanation

Let's set up the ratio of harvest to orchard size: Harvest / Orchard size = 14,000 pounds / 8 acres

Now, let's use the same ratio to find the expected harvest from a 30-acre orchard: Expected harvest / Orchard size = x pounds / 30 acres.

We can set up a proportion using the ratios: (14,000 pounds / 8 acres) = (x pounds / 30 acres) which can also be written as 8 / 14,000 = 30 / x.

Hence option B is correct.

27. In the equation x + y = 4, what is the value of y * x if y =2?

2

4

6

8

Applying value of y to the first equation,

x + 2 = 4

x = 2

Hence, x * y = 2 * 2 = 4

Explanation

Applying value of y to the first equation,

x + 2 = 4

x = 2

Hence, x * y = 2 * 2 = 4

28. Which of the following fractions is closest to 0?

-5/12

3/5

1/3

-2/7

To find the fraction closest to 0, we look at the absolute values of the fractions, as values closer to zero have smaller absolute values.

Let's convert the fractions to their decimal equivalents:

-5/12 ≈ -0.42

3/5 = 0.6

1/3 ≈ 0.33

-2/7 ≈ -0.29

When comparing these, -2/7 is the closest to 0, since -0.29 has the smallest absolute value compared to the other options. Thus, -2/7 is the closest fraction to 0.

Explanation

To find the fraction closest to 0, we look at the absolute values of the fractions, as values closer to zero have smaller absolute values.

Let's convert the fractions to their decimal equivalents:

-5/12 ≈ -0.42

3/5 = 0.6

1/3 ≈ 0.33

-2/7 ≈ -0.29

When comparing these, -2/7 is the closest to 0, since -0.29 has the smallest absolute value compared to the other options. Thus, -2/7 is the closest fraction to 0.

29. Triangle ABC is similar to Triangle DEF . What is the length of DF ? BC=8 AC=6 EF=4

2 meters

3 meters

4 meters

6 meters

Since triangles ABC and DEF are similar, their corresponding sides are proportional.

AC / BC = DF / EF

6 / 8 = DF / 4

DF = 3

Explanation

Since triangles ABC and DEF are similar, their corresponding sides are proportional.

AC / BC = DF / EF

6 / 8 = DF / 4

DF = 3

30. Which equation could be used to find the area in square inches of a circle with a radius of 8 inches?

A=8xπ

A=πx8 to the power of 2

A=8xπ to the power of 2

None of the Above

The formula for the area of a circle is given by A=πr^2

Given the radius r = 8 inches, the equation to find the area in square inches of a circle with this radius is: A=π×(8)^2

Explanation

The formula for the area of a circle is given by A=πr^2

Given the radius r = 8 inches, the equation to find the area in square inches of a circle with this radius is: A=π×(8)^2