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Q. A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how many cows are there?

A. 8
B. 10
C. 12
D. 14

Solution

Let the number of chickens be c and the number of cows be k. We have the equations: c + k = 20 and 2c + 4k = 56. Solving these gives k = 10.

Correct Answer: B — 10

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Q. A farmer has chickens and cows. If there are 50 animals in total and the number of cows is 10 more than the number of chickens, how many cows are there?

A. 20
B. 30
C. 25
D. 15

Solution

Let the number of chickens be x. Then the number of cows is x + 10. The equation is x + (x + 10) = 50. Solving gives 2x + 10 = 50, so 2x = 40, x = 20. Therefore, cows = x + 10 = 30.

Correct Answer: A — 20

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Q. A fruit seller has apples and oranges. If the total number of fruits is 80 and the number of apples is 3 times the number of oranges, how many apples are there?

A. 60
B. 30
C. 40
D. 50

Solution

Let the number of oranges be x. Then the number of apples is 3x. The equation is x + 3x = 80. Solving gives 4x = 80, so x = 20. Therefore, apples = 3x = 60.

Correct Answer: A — 60

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Q. A garden is 10 m long and 4 m wide. What is its area?

A. 40 m²
B. 44 m²
C. 50 m²
D. 30 m²

Solution

Area = length × width = 10 m × 4 m = 40 m².

Correct Answer: A — 40 m²

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Q. A garden is 10 m long and 6 m wide. What is its area?

A. 60 m²
B. 40 m²
C. 50 m²
D. 70 m²

Solution

Area = length × width = 10 m × 6 m = 60 m².

Correct Answer: A — 60 m²

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Q. A garden is 10 meters long and 6 meters wide. What is the area of the garden?

A. 60 m²
B. 70 m²
C. 80 m²
D. 90 m²

Solution

Area = length × width = 10 m × 6 m = 60 m².

Correct Answer: A — 60 m²

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Q. A garden is 6 m long and 4 m wide. What is its area?

A. 24 m²
B. 20 m²
C. 30 m²
D. 18 m²

Solution

Area = length × width = 6 m × 4 m = 24 m².

Correct Answer: A — 24 m²

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Q. A garden is 8 m long and 3 m wide. What is its perimeter?

A. 22 m
B. 24 m
C. 26 m
D. 30 m

Solution

Perimeter = 2 × (length + width) = 2 × (8 m + 3 m) = 22 m.

Correct Answer: A — 22 m

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Q. A garden is 8 m long and 3 m wide. What is the perimeter of the garden?

A. 22 m
B. 24 m
C. 26 m
D. 28 m

Solution

Perimeter = 2 × (length + width) = 2 × (8 m + 3 m) = 22 m.

Correct Answer: B — 24 m

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Q. A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?

A. 20√3 meters
B. 40 meters
C. 30 meters
D. 50 meters

Solution

Using tan(60) = 40/distance, distance = 40/tan(60) = 40/√3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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Q. A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 meters away from the wall, what is the height at which the ladder touches the wall?

A. 8 meters
B. 6 meters
C. 10 meters
D. 4 meters

Solution

Using Pythagorean theorem: height = √(10² - 6²) = √(100 - 36) = √64 = 8 meters.

Correct Answer: A — 8 meters

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Q. A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters from the wall, what is the angle of elevation of the ladder?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using cos(θ) = adjacent/hypotenuse, cos(θ) = 7/25. Therefore, θ = cos⁻¹(7/25) which is approximately 60 degrees.

Correct Answer: C — 60 degrees

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Q. A number decreased by 7 equals 12. What is the number?

A. 5
B. 19
C. 7
D. 12

Solution

Let the number be x. Then x - 7 = 12. Add 7 to both sides: x = 19.

Correct Answer: B — 19

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Q. A number decreased by 7 is equal to 3. What is the number?

A. 8
B. 9
C. 10
D. 11

Solution

Let the number be x. The equation is x - 7 = 3. Adding 7 to both sides gives x = 10.

Correct Answer: A — 8

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Q. A number is decreased by 4 and then multiplied by 3. The result is 18. What is the number?

A. 8
B. 10
C. 6
D. 7

Solution

Let the number be x. Then, 3(x - 4) = 18. Dividing by 3 gives x - 4 = 6. Adding 4 gives x = 10.

Correct Answer: A — 8

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Q. A number is decreased by 9 and then multiplied by 2 to give 10. What is the number?

A. 14
B. 15
C. 16
D. 17

Solution

Let the number be x. The equation is 2(x - 9) = 10. Dividing by 2 gives x - 9 = 5, so x = 14.

Correct Answer: A — 14

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Q. A number is decreased by 9 and then multiplied by 4 to give 28. What is the number?

A. 5
B. 7
C. 9
D. 11

Solution

Let the number be x. The equation is 4(x - 9) = 28. Dividing by 4 gives x - 9 = 7, so x = 16.

Correct Answer: C — 9

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Q. A number is divided by 2 and then increased by 3. The result is 10. What is the number?

A. 10
B. 14
C. 12
D. 8

Solution

Let the number be x. Then, x/2 + 3 = 10. Subtracting 3 from both sides gives x/2 = 7. Multiplying by 2 gives x = 14.

Correct Answer: B — 14

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Q. A number is divided by 2 and then increased by 6 to equal 10. What is the number?

A. 4
B. 6
C. 8
D. 10

Solution

Let the number be x. The equation is (x / 2) + 6 = 10. Subtracting 6 from both sides gives x / 2 = 4. Multiplying by 2 gives x = 8.

Correct Answer: A — 4

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Q. A number is divided by 2 and then increased by 6 to get 10. What is the number?

A. 4
B. 6
C. 8
D. 10

Solution

Let the number be x. The equation is (x / 2) + 6 = 10. Subtracting 6 from both sides gives x / 2 = 4. Multiplying by 2 gives x = 8.

Correct Answer: C — 8

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Q. A number is divided by 2 and then increased by 7 to equal 15. What is the number?

A. 10
B. 12
C. 14
D. 16

Solution

Let the number be x. The equation is x/2 + 7 = 15. Subtracting 7 gives x/2 = 8, so x = 16.

Correct Answer: A — 10

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Q. A number is divided by 4 and then increased by 6 to equal 10. What is the number?

A. 8
B. 12
C. 16
D. 20

Solution

Let the number be x. The equation is x/4 + 6 = 10. Subtracting 6 from both sides gives x/4 = 4. Multiplying by 4 gives x = 16.

Correct Answer: A — 8

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Q. A number is increased by 15 and the result is 45. What is the number?

A. 30
B. 15
C. 45
D. 60

Solution

Let the number be x. Then x + 15 = 45. Subtract 15 from both sides: x = 30.

Correct Answer: A — 30

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Q. A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?

A. 80
B. 90
C. 100
D. 110

Solution

Let the original number be x. The equation is: x * 1.25 * 0.8 = 96. Simplifying gives x = 96 / 1 = 120, so the original number is 100.

Correct Answer: C — 100

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Q. A number is increased by 5 and then multiplied by 3 to give 24. What is the number?

A. 1
B. 3
C. 5
D. 7

Solution

Let the number be x. The equation is 3(x + 5) = 24. Simplifying gives 3x + 15 = 24. Subtract 15 from both sides: 3x = 9. Dividing by 3 gives x = 3.

Correct Answer: B — 3

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Q. A number is increased by 5 and then multiplied by 3. The result is 24. What is the number?

A. 1
B. 3
C. 5
D. 7

Solution

Let the number be x. The equation is 3(x + 5) = 24. Simplifying gives 3x + 15 = 24. Subtracting 15 from both sides gives 3x = 9. Dividing by 3 gives x = 3.

Correct Answer: B — 3

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Q. A number is multiplied by 3 and then decreased by 5. The result is 16. What is the number?

A. 7
B. 5
C. 10
D. 8

Solution

Let the number be x. Then, 3x - 5 = 16. Adding 5 to both sides gives 3x = 21. Dividing by 3 gives x = 7.

Correct Answer: A — 7

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Q. A number is multiplied by 4 and then decreased by 8 to equal 16. What is the number?

A. 4
B. 6
C. 8
D. 10

Solution

Let the number be x. The equation is 4x - 8 = 16. Adding 8 to both sides gives 4x = 24. Dividing by 4 gives x = 6.

Correct Answer: C — 8

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Q. A number is subtracted from 15 and the result is 9. What is the number?

A. 4
B. 5
C. 6
D. 7

Solution

Let the number be x. The equation is 15 - x = 9. Subtracting 15 from both sides gives -x = -6. Multiplying by -1 gives x = 6.

Correct Answer: B — 5

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Q. A number is tripled and then increased by 2 to equal 20. What is the number?

A. 5
B. 6
C. 7
D. 8

Solution

Let the number be x. The equation is 3x + 2 = 20. Subtracting 2 gives 3x = 18, so x = 6.

Correct Answer: B — 6

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