Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If a train travels 100 km in 1 hour and 30 minutes, what is its average speed?

A. 60 km/h
B. 70 km/h
C. 80 km/h
D. 90 km/h

Solution

Average Speed = Total Distance / Total Time = 100 km / 1.5 hours = 66.67 km/h.

Correct Answer: A — 60 km/h

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Q. If a train travels 120 km in 2 hours, what is its average speed?

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 80 km/h

Solution

Average speed = Total distance / Total time = 120 km / 2 hours = 60 km/h.

Correct Answer: B — 60 km/h

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Q. If a train travels 150 km at a speed of 75 km/h, how long will it take to reach its destination?

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

Solution

Time = Distance / Speed = 150 km / 75 km/h = 2 hours.

Correct Answer: C — 3 hours

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Q. If a train travels 150 km in 2 hours, what is its average speed?

A. 60 km/h
B. 70 km/h
C. 75 km/h
D. 80 km/h

Solution

Average Speed = Total Distance / Total Time = 150 km / 2 hours = 75 km/h.

Correct Answer: A — 60 km/h

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Q. If a train travels 240 km in 3 hours, what is the percentage increase in speed if it travels the same distance in 2 hours?

A. 20%
B. 25%
C. 30%
D. 40%

Solution

Initial Speed = 240 km / 3 hours = 80 km/h; New Speed = 240 km / 2 hours = 120 km/h; Percentage Increase = ((120 - 80) / 80) * 100 = 50%.

Correct Answer: B — 25%

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Q. If a train travels 300 km in 4 hours, what is the percentage increase in speed if it travels the same distance in 3 hours?

A. 25%
B. 33.33%
C. 50%
D. 75%

Solution

Initial speed = 300 km / 4 hours = 75 km/h. New speed = 300 km / 3 hours = 100 km/h. Percentage increase = ((100 - 75) / 75) * 100 = 33.33%.

Correct Answer: B — 33.33%

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Q. If a train travels 300 km in 5 hours, what is its average speed?

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 80 km/h

Solution

Average Speed = Total Distance / Total Time = 300 km / 5 h = 60 km/h.

Correct Answer: B — 60 km/h

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Q. If a train travels at a speed of 90 km/h, how long will it take to cover 270 km?

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

Solution

Time = Distance / Speed = 270 km / 90 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. If a worker can complete a job in 10 days, how much of the job can he complete in 2 days?

A. 1/5
B. 1/10
C. 1/2
D. 1/4

Solution

Work done in 1 day = 1/10. Work done in 2 days = 2/10 = 1/5.

Correct Answer: A — 1/5

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Q. If a worker can complete a job in 10 days, how much of the job can he complete in 3 days?

A. 1/10
B. 1/5
C. 3/10
D. 3/5

Solution

In 1 day, the worker completes 1/10 of the job. In 3 days, he completes 3 * (1/10) = 3/10.

Correct Answer: C — 3/10

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Q. If a worker can complete a task in 10 hours, how much of the task can he complete in 2.5 hours?

A. 0.2
B. 0.25
C. 0.3
D. 0.5

Solution

In 2.5 hours, the worker completes (2.5/10) = 0.25 of the task.

Correct Answer: B — 0.25

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Q. If a year starts on a Friday, what day of the week will it end?

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

Solution

A non-leap year has 365 days, which is 52 weeks and 1 day. Therefore, if the year starts on a Friday, it will end on a Saturday.

Correct Answer: B — Saturday

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Q. If a year starts on a Wednesday, what day of the week will it end?

A. Wednesday
B. Thursday
C. Friday
D. Saturday

Solution

A non-leap year has 365 days, which is 52 weeks and 1 day. Therefore, if the year starts on a Wednesday, it will end on a Wednesday.

Correct Answer: A — Wednesday

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Q. If A, B, and C invest $15,000, $25,000, and $10,000 respectively, what is the total profit if they earn $18,000?

A. $7,200
B. $6,000
C. $8,000
D. $9,000

Solution

Total investment = 15000 + 25000 + 10000 = 50000. Profit share for C = (10000/50000) * 18000 = $3,600.

Correct Answer: D — $9,000

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Q. If A, B, and C invest in a business in the ratio 1:2:3 and the total profit is $1200, how much does A receive?

A. $200
B. $300
C. $400
D. $500

Solution

Total parts = 1 + 2 + 3 = 6. A's share = (1/6) * 1200 = $200.

Correct Answer: C — $400

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Q. If A, B, and C invest in a business in the ratio 4:5:6 and the total profit is $1500, how much does C receive?

A. $600
B. $500
C. $400
D. $700

Solution

Total parts = 4 + 5 + 6 = 15. C's share = (6/15) * 1500 = $600.

Correct Answer: A — $600

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Q. If A, B, and C invest in a business with amounts of $15,000, $25,000, and $10,000 respectively, what is the profit share of B if the total profit is $50,000?

A. $20,000
B. $25,000
C. $15,000
D. $10,000

Solution

Total investment = 15000 + 25000 + 10000 = 50000. B's share = 25000/50000 * 50000 = $25,000.

Correct Answer: A — $20,000

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Q. If an amount of $1200 is invested at a compound interest rate of 5% per annum, what will be the total amount after 5 years?

A. $1530.00
B. $1500.00
C. $1550.00
D. $1600.00

Solution

Total Amount = 1200(1 + 0.05)^5 = 1200(1.27628156) = 1531.54

Correct Answer: A — $1530.00

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Q. If an investor earns $120 as interest on a stock worth $800 at a simple interest rate of 5% per annum, how long did the investment last?

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

Solution

Time = (Interest / (Principal * Rate)) = 120 / (800 * 0.05) = 120 / 40 = 3 years

Correct Answer: C — 4 years

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Q. If I is 10 years older than J and the sum of their ages is 70 years, how old is I?

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

Solution

Let J's age be x. Then I's age is x + 10. So, x + (x + 10) = 70. Solving gives x = 30, hence I = 40.

Correct Answer: C — 40

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Q. If I is 3 years older than J and the sum of their ages is 45 years, what is I's age?

A. 21
B. 22
C. 23
D. 24

Solution

Let J's age be x. Then I's age is x + 3. So, x + (x + 3) = 45. Solving gives x = 21, thus I = 24.

Correct Answer: C — 23

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Q. If I is 5 years older than J and the sum of their ages is 45, what is J's age?

A. 20
B. 22
C. 25
D. 23

Solution

Let J's age be x. Then I's age is x + 5. So, x + (x + 5) = 45. Solving gives x = 20.

Correct Answer: B — 22

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Q. If it is 6:00 PM now, what time will it be after 3 hours and 45 minutes?

A. 9:45 PM
B. 9:15 PM
C. 8:45 PM
D. 8:15 PM

Solution

Adding 3 hours and 45 minutes to 6:00 PM gives 9:45 PM.

Correct Answer: A — 9:45 PM

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Q. If it is 6:00 PM now, what will be the time after 3 hours and 45 minutes?

A. 9:45 PM
B. 9:15 PM
C. 8:45 PM
D. 8:15 PM

Solution

Adding 3 hours and 45 minutes to 6:00 PM gives 9:45 PM.

Correct Answer: A — 9:45 PM

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Q. If it is 9:15, what is the angle between the hour and minute hands?

A. 52.5 degrees
B. 90 degrees
C. 75 degrees
D. 105 degrees

Solution

At 9:15, the hour hand is at 97.5 degrees (9*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: A — 52.5 degrees

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Q. If January 1, 2023 is a Sunday, what day of the week will January 1, 2024 be?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Solution

2023 is not a leap year, so it has 365 days. 365 days = 52 weeks + 1 day. Therefore, January 1, 2024 will be one day after Sunday, which is Monday.

Correct Answer: A — Monday

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Q. If log10(0.1) = z, what is the value of z?

A. -1
B. 0
C. 1
D. 2

Solution

log10(0.1) = -1, so z = -1.

Correct Answer: A — -1

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Q. If log10(1) = b, what is the value of b?

A. 0
B. 1
C. 2
D. 3

Solution

log10(1) = 0, since 10^0 = 1.

Correct Answer: A — 0

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Q. If log10(100) = x, what is the value of x?

A. 1
B. 2
C. 0
D. 3

Solution

log10(100) = log10(10^2) = 2.

Correct Answer: B — 2

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Q. If log10(1000) = b, what is the value of b?

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

Solution

log10(1000) = 3, so b = 3.

Correct Answer: C — 3

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Arithmetic Aptitude

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