Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A circular garden has a radius of 7 meters. What is the area of the garden in square meters? (Use π = 22/7)

A. 154
B. 144
C. 138
D. 160

Solution

Area = π × radius² = (22/7) × 7² = (22/7) × 49 = 154 square meters.

Correct Answer: A — 154

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Q. A circular park has a radius of 7 meters. What is the area of the park in square meters? (Use π = 22/7)

A. 154
B. 144
C. 160
D. 150

Solution

Area = πr² = (22/7) × 7² = (22/7) × 49 = 154 square meters.

Correct Answer: A — 154

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Q. A class has 20 students with an average height of 150 cm. If 5 new students with an average height of 160 cm join, what is the new average height?

A. 152
B. 154
C. 156
D. 158

Solution

Total height of 20 students = 20 * 150 = 3000. Total height of 5 new students = 5 * 160 = 800. New total = 3000 + 800 = 3800. New average = 3800 / 25 = 152.

Correct Answer: C — 156

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Q. A class has 30 students with an average score of 75. If one student scores 90, what will be the new average?

A. 75.5
B. 76
C. 76.5
D. 77

Solution

New total = (75 * 30 + 90) / 31 = (2250 + 90) / 31 = 2340 / 31 = 76.5.

Correct Answer: C — 76.5

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Q. A class has 30 students. If the average score of the class is 75 and one student scored 90, what will be the new average if that student is removed?

A. 74
B. 75
C. 76
D. 77

Solution

Total score = 30 * 75 = 2250. New total = 2250 - 90 = 2160. New average = 2160 / 29 = 74.48, approximately 74.

Correct Answer: C — 76

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Q. A class has 30 students. If the average score of the class is 75 and one student scored 90, what is the average score of the remaining students?

A. 72
B. 74
C. 76
D. 78

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of remaining 29 students = 2250 - 90 = 2160. Average of remaining = 2160 / 29 = 74.48, approximately 74.

Correct Answer: B — 74

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Q. A class has 30 students. If the average score of the class is 75 and one student scores 90, what is the average score of the remaining students?

A. 74
B. 75
C. 76
D. 77

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of remaining 29 students = 2250 - 90 = 2160. Average = 2160 / 29 = 74.48, approximately 74.

Correct Answer: C — 76

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Q. A class of 30 students has an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student?

A. 80
B. 85
C. 90
D. 95

Solution

The total score of 30 students is 30 * 75 = 2250. After the new student joins, the total score becomes 31 * 76 = 2356. Therefore, the new student's score is 2356 - 2250 = 106.

Correct Answer: B — 85

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Q. A clock gains 5 minutes every hour. If it shows 10:00 AM now, what will be the actual time when it shows 12:00 PM?

A. 11:30 AM
B. 11:50 AM
C. 12:10 PM
D. 12:20 PM

Solution

In 2 hours, the clock will gain 10 minutes (5 minutes/hour * 2 hours). So, when the clock shows 12:00 PM, the actual time will be 12:00 PM - 10 minutes = 11:50 AM.

Correct Answer: B — 11:50 AM

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Q. A clock shows 3:15. What is the angle between the hour and minute hands?

A. 45 degrees
B. 90 degrees
C. 135 degrees
D. 75 degrees

Solution

At 3:15, the hour hand is at 97.5 degrees (3*30 + 15*0.5) and the minute hand is at 90 degrees. The angle between them is |97.5 - 90| = 7.5 degrees.

Correct Answer: D — 75 degrees

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Q. A clock shows 8:00. What will be the angle between the hour and minute hands at 8:30?

A. 180 degrees
B. 165 degrees
C. 150 degrees
D. 135 degrees

Solution

At 8:30, the hour hand is at 255 degrees (8 * 30 + 30 * 0.5) and the minute hand is at 180 degrees (30 * 6). The angle between them is |255 - 180| = 75 degrees.

Correct Answer: B — 165 degrees

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Q. A company has 100 employees with an average salary of $5000. If 10 employees leave with an average salary of $6000, what is the new average salary?

A. $4900
B. $4950
C. $5000
D. $5050

Solution

Total salary of 100 employees = 100 * 5000 = $500000. Total salary of 10 employees leaving = 10 * 6000 = $60000. New total salary = 500000 - 60000 = $440000. New average = 440000 / 90 = $4888.89, which rounds to $4900.

Correct Answer: B — $4950

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Q. A company increased the salary of its employees by 12%. If an employee's current salary is $1,500, what will be the new salary?

A. $1,620
B. $1,680
C. $1,700
D. $1,800

Solution

New salary = 1500 + (12/100)*1500 = 1500 + 180 = $1,680.

Correct Answer: B — $1,680

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Q. A company increased the salary of its employees by 15%. If an employee's current salary is $2000, what will be the new salary after the increase?

A. $2200
B. $2300
C. $2400
D. $2500

Solution

New salary = Current salary + (15% of Current salary) = 2000 + (0.15 * 2000) = 2000 + 300 = 2300.

Correct Answer: A — $2200

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Q. A cone has a base radius of 5 cm and a height of 12 cm. What is the total surface area of the cone?

A. 130 cm²
B. 150 cm²
C. 180 cm²
D. 200 cm²

Solution

Total Surface Area = πr(r + l), where l = √(r² + h²) = √(5² + 12²) = √169 = 13. Total Surface Area = π * 5 * (5 + 13) = 90π cm².

Correct Answer: B — 150 cm²

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Q. A cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone?

A. 12 cm³
B. 36 cm³
C. 24 cm³
D. 18 cm³

Solution

Volume = (1/3)πr²h = (1/3) * π * 3² * 4 = (1/3) * 3.14 * 9 * 4 = 37.68 cm³.

Correct Answer: C — 24 cm³

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Q. A container has 30 liters of a mixture of milk and water in the ratio 2:1. How much water is in the mixture?

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

Solution

In a 2:1 ratio, for every 3 parts, 1 part is water. Therefore, water = (1/3) * 30 = 10 liters.

Correct Answer: A — 10 liters

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Q. A container has 50 liters of a mixture of juice and water in the ratio 4:1. How much juice is in the mixture?

A. 30 liters
B. 35 liters
C. 40 liters
D. 45 liters

Solution

In a 4:1 ratio, total parts = 4 + 1 = 5. Juice = (4/5) * 50 = 40 liters.

Correct Answer: C — 40 liters

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Q. A container has 60 liters of a mixture of juice and water in the ratio 4:1. How much juice is in the mixture?

A. 48 liters
B. 12 liters
C. 36 liters
D. 24 liters

Solution

Juice = (4/5) * 60 = 48 liters.

Correct Answer: A — 48 liters

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Q. A container has 60 liters of a solution that is 15% acid. If 10 liters of this solution is replaced with water, what is the new percentage of acid in the solution?

A. 10%
B. 12%
C. 15%
D. 18%

Solution

Initial acid = 0.15 * 60 = 9 liters. After removing 10 liters, acid left = 9 - 0.15 * 10 = 7.5 liters. New volume = 60 liters. New percentage = (7.5/60) * 100 = 12.5%.

Correct Answer: A — 10%

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Q. A container has 80 liters of a solution that is 10% acid. If 20 liters of this solution is replaced with pure acid, what will be the new concentration of acid in the solution?

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

Solution

Initial acid = 10% of 80 = 8 liters. After removing 20 liters, acid left = 8 - 2 = 6 liters. Adding 20 liters of pure acid gives 6 + 20 = 26 liters of acid in 80 liters. New concentration = (26/80) * 100 = 32.5%.

Correct Answer: C — 25%

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Q. A container has a mixture of 80 liters of liquid, which is 25% alcohol. How much alcohol is in the container?

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

Solution

Alcohol = 25% of 80 liters = 0.25 * 80 = 20 liters.

Correct Answer: B — 15 liters

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Q. A cube has a side length of 4 cm. What is the volume of the cube?

A. 16 cm³
B. 64 cm³
C. 48 cm³
D. 32 cm³

Solution

Volume = side³ = 4³ = 64 cm³.

Correct Answer: B — 64 cm³

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Q. A cyclist covers a distance of 30 km in 1.5 hours. What is the cyclist's speed?

A. 18 km/h
B. 20 km/h
C. 22 km/h
D. 25 km/h

Solution

Speed = Distance / Time = 30 km / 1.5 h = 20 km/h.

Correct Answer: B — 20 km/h

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Q. A cyclist covers a distance of 45 km in 1.5 hours. What is the cyclist's speed?

A. 25 km/h
B. 30 km/h
C. 35 km/h
D. 40 km/h

Solution

Speed = Distance / Time = 45 km / 1.5 h = 30 km/h.

Correct Answer: B — 30 km/h

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Q. A cyclist covers a distance of 90 km in 3 hours. What is his average speed?

A. 25 km/h
B. 30 km/h
C. 20 km/h
D. 35 km/h

Solution

Average speed = Total distance / Total time = 90 km / 3 hours = 30 km/h.

Correct Answer: B — 30 km/h

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Q. A cyclist travels at a speed of 15 km/h. How long will it take to cover 45 km?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

Time = Distance / Speed = 45 km / 15 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the volume of the cylinder?

A. 40π cm³
B. 20π cm³
C. 30π cm³
D. 10π cm³

Solution

Volume = πr²h = π * 2² * 10 = π * 4 * 10 = 40π cm³.

Correct Answer: A — 40π cm³

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Q. A cylinder has a radius of 5 cm and a height of 7 cm. What is the total surface area of the cylinder?

A. 376.99 cm²
B. 314.16 cm²
C. 251.33 cm²
D. 157.08 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (7 + 5) = 2 * 3.14 * 5 * 12 = 376.99 cm².

Correct Answer: A — 376.99 cm²

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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank (including the top and bottom)?

A. 56.52 m²
B. 94.25 m²
C. 113.10 m²
D. 78.54 m²

Solution

Surface Area = 2πr(h + r) = 2 * π * 3 * (5 + 3) = 2 * 3.14 * 3 * 8 = 150.72 m².

Correct Answer: B — 94.25 m²

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Arithmetic Aptitude

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