Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If a certain year is a leap year, how many days are there in that year?

A. 364
B. 365
C. 366
D. 367

Solution

A leap year has 366 days.

Correct Answer: C — 366

Q. If a clock is set 10 minutes fast, what will be the actual time when it shows 5:50?

A. 5:40
B. 5:50
C. 6:00
D. 5:30

Solution

If the clock is 10 minutes fast, when it shows 5:50, the actual time is 5:50 - 10 minutes = 5:40.

Correct Answer: A — 5:40

Q. If a clock loses 2 minutes every hour, how much time will it show after 5 hours if it started at 12:00?

A. 4:00
B. 4:10
C. 4:20
D. 4:30

Solution

In 5 hours, the clock will lose 10 minutes (2 minutes/hour * 5 hours). So, it will show 12:00 - 10 minutes = 11:50.

Correct Answer: B — 4:10

Q. If a clock shows 12:45, what is the angle between the hour and minute hands?

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

Solution

At 12:45, the hour hand is at 337.5 degrees (12 * 30 + 45 * 0.5) and the minute hand is at 270 degrees (45 * 6). The angle between them is |337.5 - 270| = 67.5 degrees.

Correct Answer: C — 165 degrees

Q. If a clock shows 3:15, what is the angle between the hour and the minute hand?

A. 7.5 degrees
B. 22.5 degrees
C. 45 degrees
D. 52.5 degrees

Solution

At 3:15, the hour hand is at 97.5 degrees (3 hours * 30 + 15 minutes * 0.5) and the minute hand is at 90 degrees (15 minutes * 6). The angle between them is |97.5 - 90| = 7.5 degrees.

Correct Answer: D — 52.5 degrees

Q. If a coin is flipped three times, what is the probability of getting exactly two heads?

A. 3/8
B. 1/2
C. 1/4
D. 1/8

Solution

The total outcomes are 2^3 = 8. The combinations for exactly 2 heads are HHT, HTH, THH, which gives us 3 favorable outcomes. So, the probability is 3/8.

Correct Answer: A — 3/8

Q. If a coin is tossed three times, what is the probability of getting at least one head?

A. 1/8
B. 1/2
C. 7/8
D. 3/8

Solution

The probability of getting no heads (all tails) is (1/2)^3 = 1/8. Therefore, the probability of getting at least one head is 1 - 1/8 = 7/8.

Correct Answer: C — 7/8

Q. If a coin is tossed three times, what is the probability of getting exactly two heads?

A. 3/8
B. 1/2
C. 1/4
D. 5/8

Solution

The number of ways to get exactly 2 heads in 3 tosses is 3 (HHT, HTH, THH). The total outcomes are 2^3 = 8. So, the probability is 3/8.

Correct Answer: A — 3/8

Q. If A invests $15,000 and B invests $25,000 in a business, and they share the profit in the ratio of their investments, what will be B's share if the total profit is $20,000?

A. $8,000
B. $10,000
C. $12,000
D. $15,000

Solution

Total investment = $15,000 + $25,000 = $40,000. B's share = 25000/40000 * 20000 = $12,500.

Correct Answer: B — $10,000

Q. If A invests $20,000 and B invests $30,000 in a business, and they earn a profit of $10,000, how much profit will A receive?

A. $4,000
B. $4,500
C. $5,000
D. $6,000

Solution

Total investment = 20000 + 30000 = 50000. A's share = 20000/50000 = 2/5. Profit for A = (2/5) * 10000 = $4,000.

Correct Answer: C — $5,000

Q. If A invests $40,000 and B invests $60,000 in a business, and they earn a profit of $20,000, how much profit will B receive?

A. $8,000
B. $12,000
C. $10,000
D. $14,000

Solution

Total investment = 40000 + 60000 = 100000. B's share = (60000/100000) * 20000 = $12,000.

Correct Answer: B — $12,000

Q. If A invests $40,000 and B invests $60,000 in a business, and they share the profit in the ratio of their investments, what will be A's share if the total profit is $30,000?

A. $10,000
B. $12,000
C. $15,000
D. $18,000

Solution

Total investment = 40000 + 60000 = 100000. A's share = 40000/100000 * 30000 = $12,000.

Correct Answer: C — $15,000

Q. If A is 3 years older than B and B is 2 years younger than C, how old is C if A is 25 years old?

A. 24
B. 26
C. 27
D. 28

Solution

If A is 25 years old, then B is 25 - 3 = 22 years old. Since B is 2 years younger than C, C is 22 + 2 = 24 years old.

Correct Answer: B — 26

Q. If a jacket is marked at $120 and is sold at a 25% discount, what is the sale price?

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

Solution

Discount = 25% of 120 = 30. Sale price = 120 - 30 = 90.

Correct Answer: A — $80

Q. If a jacket is marked at $150 and is sold for $120, what is the discount percentage?

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

Solution

Discount = 150 - 120 = 30. Discount percentage = (30 / 150) * 100 = 20%.

Correct Answer: C — 25%

Q. If a kite is flying at a height of 100 meters and the angle of elevation from a point on the ground is 60 degrees, how far is the point from the base of the kite?

A. 50 meters
B. 100 meters
C. 150 meters
D. 200 meters

Solution

Distance = height / tan(60) = 100 / √3 = 100/√3 = 50 meters

Correct Answer: A — 50 meters

Q. If a kite is flying at a height of 60 meters and 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's vertical line?

A. 30 meters
B. 20√3 meters
C. 60 meters
D. 40 meters

Solution

Distance = height / tan(angle) = 60 / (√3) = 20√3 meters.

Correct Answer: B — 20√3 meters

Q. If a man earns $1200 after a 20% raise, what was his original salary?

A. $900
B. $1000
C. $1100
D. $1200

Solution

Let the original salary be x. After a 20% raise, x + 0.2x = 1.2x = 1200. Thus, x = 1200 / 1.2 = 1000.

Correct Answer: B — $1000

Q. If a man earns $1200 after a 20% raise, what was his salary before the raise?

A. $900
B. $1000
C. $1100
D. $1200

Solution

Let the original salary be x. After a 20% raise, the salary is x + 0.2x = 1.2x. Given 1.2x = 1200, we find x = 1200 / 1.2 = 1000.

Correct Answer: B — $1000

Q. If a mixture of 100 liters has 70% water, how much water is in the mixture?

A. 60 liters
B. 70 liters
C. 80 liters
D. 90 liters

Solution

Water = 70% of 100 liters = 0.7 * 100 = 70 liters.

Correct Answer: B — 70 liters

Q. If a month has 30 days and starts on a Friday, what day of the week will the last day of the month fall on?

A. Friday
B. Saturday
C. Sunday
D. Monday

Solution

30 days = 4 weeks + 2 days. If the month starts on a Friday, the last day will be 2 days later, which is a Saturday.

Correct Answer: B — Saturday

Q. If a month has 30 days, how many weeks are there in that month?

A. 4
B. 4.5
C. 5
D. 5.5

Solution

30 days = 4 weeks + 2 days, which is approximately 4.29 weeks, but the closest whole number is 4 weeks.

Correct Answer: C — 5

Q. If a mother is 6 times as old as her daughter now, and in 6 years, she will be 4 times as old as her daughter, how old is the daughter now?

A. 6
B. 4
C. 5
D. 3

Solution

Let the daughter's age be x. Then the mother's age is 6x. In 6 years, the mother will be 6x + 6 and the daughter will be x + 6. The equation is 6x + 6 = 4(x + 6), which simplifies to 6x + 6 = 4x + 24, so 2x = 18, and x = 9.

Correct Answer: C — 5

Q. If a number is divided by 6, the remainder is 4. What is the number?

A. 10
B. 16
C. 22
D. 28

Solution

A number that gives a remainder of 4 when divided by 6 can be expressed as 6k + 4. For k = 2, the number is 6*2 + 4 = 16.

Correct Answer: B — 16

Q. If a number is multiplied by 3 and then decreased by 9, the result is 0. What is the number?

A. 1
B. 2
C. 3
D. 4

Solution

Let the number be x. The equation is 3x - 9 = 0. Solving gives x = 3.

Correct Answer: C — 3

Q. If a number is multiplied by 9 and then decreased by 9, the result is 72. What is the number?

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

Solution

Let the number be x. The equation is 9x - 9 = 72. Adding 9 to both sides gives 9x = 81, so x = 81/9 = 9.

Correct Answer: A — 8

Q. If a person earns $1200 after a 20% raise, what was his salary before the raise?

A. $1000
B. $1100
C. $900
D. $950

Solution

Let the original salary be x. After a 20% raise, the salary is x + 0.2x = 1.2x. Therefore, 1.2x = 1200, so x = 1200 / 1.2 = $1000.

Correct Answer: A — $1000

Q. If a person earns $5000 and spends 60% of it, how much does he save?

A. $1500
B. $2000
C. $2500
D. $3000

Solution

Spending = 60% of 5000 = 3000. Savings = 5000 - 3000 = $2000.

Correct Answer: B — $2000

Q. If a person is 20 meters away from a tree and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

A. 10 meters
B. 20 meters
C. 30 meters
D. 40 meters

Solution

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

Correct Answer: B — 20 meters

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

A. 7.5 meters
B. 10 meters
C. 12.5 meters
D. 15 meters

Solution

Height = distance * tan(30) = 15 * (1/√3) = 15/√3 = 5√3 meters ≈ 7.5 meters.

Correct Answer: A — 7.5 meters

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