Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If y = sqrt(4x^2 + 1), find dy/dx.

A. (4x)/(sqrt(4x^2 + 1))
B. (2x)/(sqrt(4x^2 + 1))
C. (8x)/(sqrt(4x^2 + 1))
D. (2)/(sqrt(4x^2 + 1))

Solution

Using the chain rule, dy/dx = (4x)/(2sqrt(4x^2 + 1)) = (4x)/(sqrt(4x^2 + 1)).

Correct Answer: A — (4x)/(sqrt(4x^2 + 1))

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Q. If y = sqrt(x^2 + 1), find dy/dx at x = 0.

A. 0
B. 1
C. 1/2
D. 1/√2

Solution

dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 0, dy/dx = (1/2)(1)^(-1/2)(0) = 0.

Correct Answer: B — 1

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Q. If y = tan(3x), find dy/dx at x = π/6.

A. 3√3
B. 3
C. √3
D. 1

Solution

dy/dx = 3sec^2(3x). At x = π/6, dy/dx = 3sec^2(π/2) = 3(∞) = undefined.

Correct Answer: A — 3√3

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Q. If y = tan(3x), find dy/dx.

A. 3sec^2(3x)
B. 3tan^2(3x)
C. sec^2(3x)
D. 3tan(3x)

Solution

Using the chain rule, dy/dx = 3sec^2(3x).

Correct Answer: A — 3sec^2(3x)

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Q. If y = x^3 * e^x, find dy/dx at x = 0.

A. 0
B. 1
C. 3
D. 6

Solution

Using product rule, dy/dx = 3x^2 * e^x + x^3 * e^x. At x = 0, dy/dx = 0 + 0 = 0.

Correct Answer: A — 0

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Q. If y = √(4x^2 + 1), find dy/dx.

A. 4x/(√(4x^2 + 1))
B. 2x/(√(4x^2 + 1))
C. 2/(√(4x^2 + 1))
D. 8x/(√(4x^2 + 1))

Solution

dy/dx = (4x)/(2√(4x^2 + 1)) = 4x/(√(4x^2 + 1)).

Correct Answer: A — 4x/(√(4x^2 + 1))

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Q. If y = √(x^2 + 1), find dy/dx at x = 1.

A. 1/√2
B. 1/2
C. 1
D. 2

Solution

dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 1, dy/dx = (1/2)(2)^(-1/2)(2) = 1/√2.

Correct Answer: A — 1/√2

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Q. If you invest $1000 at an interest rate of 8% compounded annually, how much will you have after 2 years?

A. $1166.40
B. $1080.00
C. $1200.00
D. $1150.00

Solution

Total Amount = 1000(1 + 0.08)^2 = 1000(1.1664) = 1166.40

Correct Answer: A — $1166.40

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Q. In 10 years, a father will be twice as old as his son. If the son is currently 10 years old, how old is the father now?

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

Solution

Let the father's current age be x. In 10 years, x + 10 = 2(10 + 10). Solving gives x = 30.

Correct Answer: B — 30

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Q. In 5 years, a man will be 3 times as old as his son. If the son is currently 5 years old, how old is the man now?

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

Solution

Let the man's current age be x. In 5 years, x + 5 = 3 * (5 + 5). Solving gives x = 25.

Correct Answer: C — 25

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Q. In 5 years, A will be 3 times as old as B. If B is currently 10 years old, how old is A now?

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

Solution

In 5 years, B will be 15. Therefore, A will be 3 * 15 = 45. So, A is currently 45 - 5 = 40 years old.

Correct Answer: B — 20

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Q. In 5 years, A will be 3 times as old as B. If B is currently 10 years old, how old will A be in 5 years?

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

Solution

In 5 years, B will be 10 + 5 = 15. A will be 3 * 15 = 45. So, A's current age is 45 - 5 = 40.

Correct Answer: C — 25

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Q. In a bag of 20 candies, 8 are chocolate. What is the probability of picking a non-chocolate candy?

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

Solution

Number of non-chocolate candies = 20 - 8 = 12. Probability = 12/20 = 3/5.

Correct Answer: A — 3/5

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Q. In a class of 30 students, 18 are girls. If a student is chosen at random, what is the probability that the student is a boy?

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

Solution

The number of boys is 30 - 18 = 12. The probability is 12/30 = 2/5.

Correct Answer: A — 1/3

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Q. In a class of 30 students, 18 are girls. If a student is selected at random, what is the probability that the student is a boy?

A. 0.4
B. 0.6
C. 0.5
D. 0.3

Solution

The number of boys is 30 - 18 = 12. The probability is 12/30 = 0.4.

Correct Answer: B — 0.6

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Q. In a class of 30 students, 18 are girls. What is the probability that a randomly selected student is a boy?

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

Solution

Number of boys = 30 - 18 = 12. Probability of boy = 12/30 = 2/5.

Correct Answer: B — 2/5

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Q. In a class of 40 students, the average height is 150 cm. If 10 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 40 students = 40 * 150 = 6000 cm. Total height of 10 new students = 10 * 160 = 1600 cm. New total height = 6000 + 1600 = 7600 cm. New average = 7600 / 50 = 152 cm.

Correct Answer: B — 154

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Q. In a class of 40 students, the average height is 150 cm. If 10 new students with an average height of 160 cm join, what will be the new average height?

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

Solution

The total height of the original students is 40 * 150 = 6000 cm. The total height of the new students is 10 * 160 = 1600 cm. The new total height is 6000 + 1600 = 7600 cm. The new average height is 7600 / 50 = 152 cm.

Correct Answer: C — 156

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Q. In a class, 60% of the students are girls. If there are 24 girls, how many students are there in total?

A. 30
B. 36
C. 40
D. 42

Solution

Let the total number of students be x. Then, 0.6x = 24. Therefore, x = 24 / 0.6 = 40.

Correct Answer: B — 36

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Q. In a class, 60% of the students are girls. If there are 30 boys, how many students are there in total?

A. 50
B. 60
C. 70
D. 80

Solution

Let the total number of students be x. Then, 40% of x = 30 (boys). So, x = 30 / 0.4 = 75. Total students = 75.

Correct Answer: B — 60

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Q. In a deck of 52 cards, what is the probability of drawing a heart?

A. 1/4
B. 1/13
C. 1/2
D. 3/13

Solution

Total hearts = 13. Probability of heart = 13/52 = 1/4.

Correct Answer: A — 1/4

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Q. In a group of 10 people, the average age is 30 years. If two new members join the group and the average age becomes 32 years, what is the average age of the new members?

A. 34
B. 36
C. 38
D. 40

Solution

Total age of 10 people = 10 * 30 = 300. New total age = 12 * 32 = 384. Age of new members = 384 - 300 = 84. Average age of new members = 84 / 2 = 42.

Correct Answer: B — 36

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Q. In a group of 5 friends, the average age is 24 years. If the age of one friend is 30 years, what is the average age of the remaining friends?

A. 22
B. 23
C. 24
D. 25

Solution

The total age of the 5 friends is 5 * 24 = 120. The total age of the remaining 4 friends is 120 - 30 = 90. The average age of the remaining friends is 90 / 4 = 22.5.

Correct Answer: B — 23

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Q. In a group of 6 friends, the average age is 22 years. If one friend leaves and the average age becomes 23 years, what is the age of the friend who left?

A. 20
B. 22
C. 24
D. 26

Solution

Total age of 6 friends = 6 * 22 = 132. Total age of 5 friends = 5 * 23 = 115. Age of friend who left = 132 - 115 = 17.

Correct Answer: C — 24

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Q. In a lottery with 100 tickets, 10 are winning tickets. What is the probability of selecting a winning ticket?

A. 1/10
B. 1/5
C. 1/20
D. 1/2

Solution

Probability of winning ticket = 10/100 = 1/10.

Correct Answer: A — 1/10

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Q. In a lottery with 100 tickets, 10 are winning tickets. What is the probability of picking a winning ticket?

A. 1/10
B. 1/5
C. 1/20
D. 1/50

Solution

Probability of picking a winning ticket = 10/100 = 1/10.

Correct Answer: A — 1/10

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Q. In a lottery with 50 tickets, 5 are winning tickets. What is the probability of picking a winning ticket?

A. 1/10
B. 1/5
C. 1/20
D. 1/50

Solution

Probability of winning ticket = 5/50 = 1/10.

Correct Answer: B — 1/5

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Q. In a lottery, there are 10 tickets, and 3 of them are winning tickets. What is the probability of picking a winning ticket?

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

Solution

The probability of picking a winning ticket is 3/10.

Correct Answer: C — 3/10

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Q. In a lottery, there are 100 tickets, and 10 of them are winning tickets. What is the probability of picking a winning ticket?

A. 1/10
B. 1/5
C. 1/20
D. 1/50

Solution

The probability of picking a winning ticket is 10/100 = 1/10.

Correct Answer: B — 1/5

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Q. In a mixture of 100 liters, the ratio of oil to water is 1:4. How much oil is in the mixture?

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

Solution

Let the amount of oil be x liters. Then, water = 4x liters. x + 4x = 100 liters, 5x = 100, x = 20 liters. Therefore, oil = 20 liters.

Correct Answer: A — 10 liters

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Arithmetic Aptitude

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