Exemption Test In Mathematics 6

1) In a school there are four boy scouts to every three girl scouts. If there are forty-two girl scouts, how many boy scouts are there?

56 boy scouts

56 girl scouts

31.5 girl scouts

31.5 boy scouts

48 boy scouts

If there are four boy scouts for every three girl scouts, and there are forty-two girl scouts, we can find the number of boy scouts by using proportions. We can set up the proportion: 4 boy scouts / 3 girl scouts = x boy scouts / 42 girl scouts. Solving for x, we find that x = (4/3) * 42 = 56. Therefore, there are 56 boy scouts.

Explanation

If there are four boy scouts for every three girl scouts, and there are forty-two girl scouts, we can find the number of boy scouts by using proportions. We can set up the proportion: 4 boy scouts / 3 girl scouts = x boy scouts / 42 girl scouts. Solving for x, we find that x = (4/3) * 42 = 56. Therefore, there are 56 boy scouts.

2) Find the value of N.N:8 = 3:4

5

4

6

3

In the given equation, N.N:8 = 3:4, the ratio of N.N to 8 is equal to the ratio of 3 to 4. To find the value of N.N, we can set up a proportion. Cross multiplying, we get N.N * 4 = 3 * 8. Simplifying further, we have N.N = 24/4, which equals 6. Therefore, the value of N.N is 6.

Explanation

In the given equation, N.N:8 = 3:4, the ratio of N.N to 8 is equal to the ratio of 3 to 4. To find the value of N.N, we can set up a proportion. Cross multiplying, we get N.N * 4 = 3 * 8. Simplifying further, we have N.N = 24/4, which equals 6. Therefore, the value of N.N is 6.

3) If it costs $90 to feed a family of 3 for one week, how much will it cost to feed a family of 5 for one week?

$180.00

$30.00

$120.00

$150.00

To find the cost of feeding a family of 5 for one week, we can use the concept of proportion. The cost of feeding a family of 3 is given as $90, so we can set up a proportion: 3/5 = 90/x, where x represents the cost of feeding a family of 5. By cross-multiplying, we get 3x = 450, and dividing both sides by 3, we find that x = 150. Therefore, it will cost $150 to feed a family of 5 for one week.

Explanation

To find the cost of feeding a family of 5 for one week, we can use the concept of proportion. The cost of feeding a family of 3 is given as $90, so we can set up a proportion: 3/5 = 90/x, where x represents the cost of feeding a family of 5. By cross-multiplying, we get 3x = 450, and dividing both sides by 3, we find that x = 150. Therefore, it will cost $150 to feed a family of 5 for one week.

4) True or False3:4 is greater than 5:8

True

False

not-available-via-ai

Explanation

not-available-via-ai

5) On a triangle, each side measures 5 cm, 10 cm, and 30 cm, respectively. In lowest terms, find the ratios of the lengths of the sides.

1:2:6

5:10:30

5:1:3

5/10/30

The given triangle has sides measuring 5 cm, 10 cm, and 30 cm. To find the ratios of the lengths of the sides in lowest terms, we can divide each side length by the greatest common divisor of all three sides. The greatest common divisor of 5, 10, and 30 is 5. Dividing each side length by 5, we get 1 cm, 2 cm, and 6 cm. Therefore, the ratios of the lengths of the sides in lowest terms are 1:2:6.

Explanation

The given triangle has sides measuring 5 cm, 10 cm, and 30 cm. To find the ratios of the lengths of the sides in lowest terms, we can divide each side length by the greatest common divisor of all three sides. The greatest common divisor of 5, 10, and 30 is 5. Dividing each side length by 5, we get 1 cm, 2 cm, and 6 cm. Therefore, the ratios of the lengths of the sides in lowest terms are 1:2:6.

6) In Canada there is one car for every 19 people. How many car tires per person are there?

2:1

4:1

40:19

None of the above

The question asks for the number of car tires per person in Canada. However, none of the given options provide a ratio or number that represents the number of car tires per person accurately. Therefore, the correct answer is "None of the above".

Explanation

The question asks for the number of car tires per person in Canada. However, none of the given options provide a ratio or number that represents the number of car tires per person accurately. Therefore, the correct answer is "None of the above".

7) Johnny has a bag full of marbles that he keeps in his desk. He has 35 red marbles and 25 green marbles. Find the ratio of red marbles to green marbles, and put it in its simplest form.

35:25

7:5

25:35

5:7

6:5

The ratio of red marbles to green marbles is 7:5. This is because there are 35 red marbles and 25 green marbles, and when simplified, the ratio becomes 7:5.

Explanation

The ratio of red marbles to green marbles is 7:5. This is because there are 35 red marbles and 25 green marbles, and when simplified, the ratio becomes 7:5.

8) To make green paint, Jack mixes yellow paint and blue paint in the ratio of three to two. If he used twelve gallons of yellow paint, how much blue paint did he use?

4

6

7

8

12

Jack mixes yellow paint and blue paint in the ratio of three to two. This means that for every three gallons of yellow paint, he uses two gallons of blue paint. If he used twelve gallons of yellow paint, he would need to use eight gallons of blue paint (12/3 * 2 = 8). Therefore, the correct answer is 8.

Explanation

Jack mixes yellow paint and blue paint in the ratio of three to two. This means that for every three gallons of yellow paint, he uses two gallons of blue paint. If he used twelve gallons of yellow paint, he would need to use eight gallons of blue paint (12/3 * 2 = 8). Therefore, the correct answer is 8.

9) Crystal mixed orange juice, fruit punch concentrate, and ginger ale in the ratio of 2:2:4 to make a special drink. To make 4 liters, how much of each ingredient should she use?

2L orange, 2L punch, 4L ginger ale

8L orange, 8L punch, 16L ginger ale

2L orange, 1L punch, 1L ginger ale

1L orange, 1L punch, 2L ginger ale

To make the special drink, Crystal needs to mix the orange juice, fruit punch concentrate, and ginger ale in a ratio of 2:2:4. This means that for every 2 parts of orange juice, she needs 2 parts of fruit punch concentrate and 4 parts of ginger ale. Since she wants to make 4 liters of the drink, she needs to divide the total amount into these ratios. Therefore, she should use 1 liter of orange juice, 1 liter of fruit punch concentrate, and 2 liters of ginger ale to make the special drink.

Explanation

To make the special drink, Crystal needs to mix the orange juice, fruit punch concentrate, and ginger ale in a ratio of 2:2:4. This means that for every 2 parts of orange juice, she needs 2 parts of fruit punch concentrate and 4 parts of ginger ale. Since she wants to make 4 liters of the drink, she needs to divide the total amount into these ratios. Therefore, she should use 1 liter of orange juice, 1 liter of fruit punch concentrate, and 2 liters of ginger ale to make the special drink.

10) A rectangle measures 20cm at its width and 5 cm at its length. Find the ratio of the length to the width to the perimeter of the rectangle in lowest form.

1:4:10

4:1:10

5:20:50

20:5:50

None of the above

The ratio of the length to the width to the perimeter of the rectangle is 1:4:10. This can be determined by dividing the length by the width, which gives a ratio of 1:4. To find the ratio of the perimeter, we add the length and width and multiply by 2, which gives a ratio of 10. Therefore, the correct answer is 1:4:10.

Explanation

The ratio of the length to the width to the perimeter of the rectangle is 1:4:10. This can be determined by dividing the length by the width, which gives a ratio of 1:4. To find the ratio of the perimeter, we add the length and width and multiply by 2, which gives a ratio of 10. Therefore, the correct answer is 1:4:10.

11) Find the value of N.18N:54 = 12:9

5

6

2

4

In the given equation, 18N:54 = 12:9, we can simplify it by dividing both sides by 6. This gives us 3N:9 = 2:3. Since the ratio on the left side is in terms of N, we can see that N must be equal to 2. Therefore, the correct answer is 4, as N is equal to 2.

Explanation

In the given equation, 18N:54 = 12:9, we can simplify it by dividing both sides by 6. This gives us 3N:9 = 2:3. Since the ratio on the left side is in terms of N, we can see that N must be equal to 2. Therefore, the correct answer is 4, as N is equal to 2.

12) One out of three students in the school owns a cat. Of these students one out of two owns a fish. What fraction of the students owns both a cat and a fish?

1/6 of all students own both a cat and a fish.

1/2 of all students own both a cat and a fish.

5/6 of all students own both a cat and a fish.

3/4 of all students own both a cat and a fish.

1/4 of all students own both a cat and a fish.

Since one out of three students in the school owns a cat, we can say that the fraction of students who own a cat is 1/3. Of these students, one out of two owns a fish, which means the fraction of students who own both a cat and a fish is 1/2 of 1/3, which simplifies to 1/6. Therefore, 1/6 of all students own both a cat and a fish.

Explanation

Since one out of three students in the school owns a cat, we can say that the fraction of students who own a cat is 1/3. Of these students, one out of two owns a fish, which means the fraction of students who own both a cat and a fish is 1/2 of 1/3, which simplifies to 1/6. Therefore, 1/6 of all students own both a cat and a fish.

13) 78 children attended a trip to the fair. 60 of them were girls. Find the ratio of the number of girls to boys.

60:18

18:60

10:3

60:78

3:10

The ratio of the number of girls to boys can be found by dividing the number of girls by the number of boys. In this case, we know that there were 78 children in total and 60 of them were girls. Therefore, the number of boys can be found by subtracting the number of girls from the total number of children: 78 - 60 = 18. So, the ratio of girls to boys is 60:18, which simplifies to 10:3.

Explanation

The ratio of the number of girls to boys can be found by dividing the number of girls by the number of boys. In this case, we know that there were 78 children in total and 60 of them were girls. Therefore, the number of boys can be found by subtracting the number of girls from the total number of children: 78 - 60 = 18. So, the ratio of girls to boys is 60:18, which simplifies to 10:3.

14) Brandon received $50 dollars for his paper route. He spent $20 dollars at the movies, and $10 dollars buying comic books then after buying $5 worth of popcorn, he saved the rest. What is the ratio of the amount of money spent buying comic books and popcorn, to the amount that saved?

10:5:15

15:15

1:1

2:1:3

1:2:3

Brandon spent a total of $10 on comic books and $5 on popcorn, which adds up to $15. He saved the rest of the money, which is $50 - $15 = $35. Therefore, the ratio of the amount of money spent on comic books and popcorn to the amount saved is 15:35, which simplifies to 1:2. The given answer, 1:1, is incorrect.

Explanation

Brandon spent a total of $10 on comic books and $5 on popcorn, which adds up to $15. He saved the rest of the money, which is $50 - $15 = $35. Therefore, the ratio of the amount of money spent on comic books and popcorn to the amount saved is 15:35, which simplifies to 1:2. The given answer, 1:1, is incorrect.

15) Matching Type.

Comparison of two numbers or quantities

A special ratio that compares two measurements with different units

A rate which the denominator is one

(53.6 +9.76) - 23.048 =

(79.345 + 35.93) - (79.345 - 35.93)

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