Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A number is increased by 20% and then decreased by 20%. What is the net change in the number?

A. 0%
B. 4%
C. 5%
D. 10%

Solution

Let the original number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 120 - 24 = 96. The net change is (96 - 100)/100 * 100% = -4%.

Correct Answer: B — 4%

Q. A number is increased by 20% and then decreased by 20%. What is the net change?

A. 0%
B. 4%
C. 5%
D. 10%

Solution

Let the number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 120 - 24 = 96. The net change is (96 - 100)/100 * 100% = -4%.

Correct Answer: A — 0%

Q. A parallelogram has a base of 12 cm and a height of 5 cm. What is its area?

A. 60 cm²
B. 50 cm²
C. 70 cm²
D. 40 cm²

Solution

Area = base × height = 12 cm × 5 cm = 60 cm².

Correct Answer: A — 60 cm²

Q. A person invests $1,000 at an interest rate of 5% per annum. How much interest will he earn in one year?

A. $40
B. $50
C. $60
D. $70

Solution

Interest = 5% of 1,000 = 50.

Correct Answer: B — $50

Q. A person is looking at the top of a 40-meter tall building from a distance of 50 meters. What is the angle of elevation?

A. 30 degrees
B. 36.87 degrees
C. 45 degrees
D. 53.13 degrees

Solution

tan(θ) = height/distance = 40/50, θ = tan⁻¹(0.8) ≈ 38.66 degrees.

Correct Answer: B — 36.87 degrees

Q. A person is standing 15 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 15√3 meters
B. 10 meters
C. 5 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 15 * (1/√3) = 15/√3 = 15√3 meters.

Correct Answer: A — 15√3 meters

Q. A person is standing 15 meters away from a tree. If the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

A. 10 meters
B. 15 meters
C. 20 meters
D. 25 meters

Solution

Height = distance * tan(angle) = 15 * 1 = 15 meters.

Correct Answer: B — 15 meters

Q. A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

A. 15√3 meters
B. 10√3 meters
C. 20 meters
D. 25 meters

Solution

Height = distance * tan(60) = 15 * √3 = 15√3 meters

Correct Answer: A — 15√3 meters

Q. A person is standing 25 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

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

Solution

Height = distance * tan(37) = 25 * 0.7536 ≈ 18.84 meters, rounded to 20 meters.

Correct Answer: B — 20 meters

Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?

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

Solution

Height = distance * tan(angle) = 25 * tan(53°) ≈ 25 * 1.327 = 20.68 meters.

Correct Answer: B — 20 meters

Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 30 degrees, what is the height of the pole?

A. 12.5 meters
B. 25 meters
C. 15√3 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 25 * (1/√3) = 25/√3 ≈ 12.5 meters.

Correct Answer: A — 12.5 meters

Q. A person is standing 25 meters away from a wall. If the angle of elevation to the top of the wall is 75 degrees, what is the height of the wall?

A. 24.5 meters
B. 25 meters
C. 26.5 meters
D. 27.5 meters

Solution

Height = distance * tan(75) = 25 * 3.732 = 93.3 meters.

Correct Answer: D — 27.5 meters

Q. A person is standing 30 meters away from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 30√3
B. 20√3
C. 10√3
D. 40√3

Solution

height = distance * tan(60) = 30 * √3 = 30√3 meters

Correct Answer: A — 30√3

Q. A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

A. 20 meters
B. 30 meters
C. 40 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 40 * 1 = 40 meters.

Correct Answer: C — 40 meters

Q. A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 20 meters
B. 23 meters
C. 30 meters
D. 35 meters

Solution

Height = distance * tan(angle) = 40 * (1/√3) = 40 / 1.732 = 23.09 meters.

Correct Answer: A — 20 meters

Q. A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?

A. 20 meters
B. 30 meters
C. 40 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 40 * 1 = 40 meters.

Correct Answer: C — 40 meters

Q. A person is standing 45 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 45 * 1 = 45 meters.

Correct Answer: B — 45 meters

Q. A person is standing 50 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 25 meters
B. 50 meters
C. 75 meters
D. 100 meters

Solution

Height = distance * tan(angle) = 50 * (1/√3) = 50/√3 meters.

Correct Answer: A — 25 meters

Q. A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

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

Solution

Height = distance * tan(angle) = 50 * tan(37°) ≈ 30 meters.

Correct Answer: A — 30 meters

Q. A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 30 degrees, what is the height of the hill?

A. 25√3 meters
B. 50 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 50 * (1/√3) = 50/√3 = 25√3 meters.

Correct Answer: A — 25√3 meters

Q. A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?

A. 25 meters
B. 50 meters
C. 35 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 50 * 1 = 50 meters.

Correct Answer: B — 50 meters

Q. A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?

A. 25 meters
B. 30 meters
C. 35 meters
D. 40 meters

Solution

Height = distance * tan(30) = 50 * (1/√3) ≈ 25 meters.

Correct Answer: A — 25 meters

Q. A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 40 * (1/√3) ≈ 20 meters.

Correct Answer: A — 20 meters

Q. A person received a 15% raise in his salary. If his new salary is $1,150, what was his old salary?

A. $1,000
B. $1,050
C. $1,100
D. $1,200

Solution

Let the old salary be x. Then, x + 0.15x = 1150. Therefore, 1.15x = 1150, x = 1150 / 1.15 = 1000.

Correct Answer: A — $1,000

Q. A person scores 80, 90, and 70 in three exams. What score does he need in the fourth exam to achieve an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Let the fourth score be x. (80 + 90 + 70 + x) / 4 = 85. Solving gives x = 100.

Correct Answer: B — 95

Q. A person spends 30% of his salary on rent and 20% on groceries. If his salary is $1,000, how much does he spend on rent?

A. $200
B. $250
C. $300
D. $350

Solution

Rent = 30% of 1000 = 0.3 * 1000 = 300.

Correct Answer: C — $300

Q. A person spends 40% of his income on rent and 30% on food. If his income is $2000, how much does he spend on rent?

A. $600
B. $700
C. $800
D. $900

Solution

Rent = 40% of 2000 = 0.4 * 2000 = 800.

Correct Answer: A — $600

Q. A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?

A. 100√3
B. 50√3
C. 75√3
D. 25√3

Solution

height = distance * tan(60) = 100 * √3 = 100√3 meters

Correct Answer: A — 100√3

Q. A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

A. 20 meters
B. 10 meters
C. 30 meters
D. 15 meters

Solution

Height = distance * tan(angle) = 20 * 1 = 20 meters.

Correct Answer: A — 20 meters

Q. A person standing 20 meters away from a wall sees the top of the wall at an angle of elevation of 30 degrees. What is the height of the wall?

A. 5 meters
B. 10 meters
C. 15 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 20 * (1/√3) = 20 / 1.732 = 11.55 meters.

Correct Answer: B — 10 meters

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