Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A is 3 years older than B. If the sum of their ages is 27, how old is B?

A. 10
B. 12
C. 13
D. 15

Solution

Let B's age be x. Then A's age is x + 3. So, x + (x + 3) = 27. Solving gives x = 12.

Correct Answer: B — 12

Q. A is 4 years older than B. If the sum of their ages is 28 years, how old is A?

A. 12
B. 14
C. 16
D. 18

Solution

Let B's age be x. Then A's age is x + 4. So, x + (x + 4) = 28. Solving gives x = 12, so A = 16.

Correct Answer: C — 16

Q. A is 5 years older than B. If the sum of their ages is 45 years, how old is B?

A. 20
B. 22
C. 25
D. 30

Solution

Let B's age be x. Then A's age is x + 5. So, x + (x + 5) = 45, which gives 2x + 5 = 45, hence 2x = 40, x = 20. Therefore, B is 20 years old.

Correct Answer: B — 22

Q. A is twice as old as B. If B is 10 years old, how old is A?

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

Solution

If B is 10 years old, then A is 2 * 10 = 20 years old.

Correct Answer: C — 20

Q. A jacket is marked at $150 but is sold at a 25% discount. What is the sale price of the jacket?

A. $100
B. $112.50
C. $125
D. $130

Solution

Discount = 25% of 150 = 37.5. Sale price = 150 - 37.5 = 112.5.

Correct Answer: B — $112.50

Q. A jar contains 4 green, 5 yellow, and 6 red marbles. What is the probability of picking a yellow marble?

A. 1/3
B. 5/15
C. 1/4
D. 1/5

Solution

The total number of marbles is 4 + 5 + 6 = 15. The probability of picking a yellow marble is 5/15 = 1/3.

Correct Answer: A — 1/3

Q. A jar contains 5 green, 3 yellow, and 2 blue marbles. What is the probability of picking a yellow marble?

A. 1/5
B. 1/4
C. 3/10
D. 1/3

Solution

Total marbles = 5 + 3 + 2 = 10. Probability of yellow marble = 3/10.

Correct Answer: C — 3/10

Q. A jar contains 5 green, 3 yellow, and 2 blue marbles. What is the probability of selecting a yellow marble?

A. 1/5
B. 1/4
C. 3/10
D. 1/3

Solution

Total marbles = 5 + 3 + 2 = 10. Probability of yellow marble = 3/10.

Correct Answer: C — 3/10

Q. A jar contains 5 green, 3 yellow, and 2 red marbles. What is the probability of randomly selecting a yellow marble?

A. 1/5
B. 1/4
C. 3/10
D. 1/3

Solution

The total number of marbles is 5 + 3 + 2 = 10. The probability of selecting a yellow marble is 3/10.

Correct Answer: C — 3/10

Q. A jar contains 5 green, 3 yellow, and 2 red marbles. What is the probability of picking a yellow marble?

A. 1/5
B. 1/4
C. 3/10
D. 1/3

Solution

The total number of marbles is 5 + 3 + 2 = 10. The probability of picking a yellow marble is 3/10.

Correct Answer: C — 3/10

Q. A jar contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is not green?

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

Solution

The total number of marbles is 5 + 3 + 2 = 10. The number of non-green marbles is 5 + 2 = 7. The probability is 7/10 = 7/10.

Correct Answer: C — 4/5

Q. A jar contains 5 red, 3 green, and 2 blue marbles. What is the probability of picking a green marble?

A. 1/5
B. 1/4
C. 3/10
D. 1/2

Solution

The total number of marbles is 5 + 3 + 2 = 10. The probability of picking a green marble is 3/10.

Correct Answer: C — 3/10

Q. A kite is flying at a height of 100 meters. If 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?

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

Solution

Distance = height / tan(angle) = 100 / √3 = 100√3/3 meters.

Correct Answer: A — 50 meters

Q. A kite is flying at a height of 100 meters. If 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 height?

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

Solution

Distance = height / tan(angle) = 100 / √3 ≈ 50 meters.

Correct Answer: A — 50 meters

Q. A kite is flying at a height of 30 meters. If 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?

A. 15√3 meters
B. 30 meters
C. 10√3 meters
D. 20 meters

Solution

Distance = height / tan(angle) = 30 / √3 = 10√3 meters.

Correct Answer: C — 10√3 meters

Q. A kite is flying at a height of 30 meters. If 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 height?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 10√3 meters

Solution

Distance = height / tan(angle) = 30 / (√3/3) = 30√3/3 = 10√3 meters.

Correct Answer: A — 15√3 meters

Q. A kite is flying at a height of 50 meters. If 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 height?

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

Solution

Distance = height / tan(angle) = 50 / √3 = 50 / 1.732 = 28.87 meters.

Correct Answer: A — 25 meters

Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground is 30 degrees, how far is the point from the base of the kite?

A. 50√3
B. 25√3
C. 75√3
D. 100√3

Solution

distance = height / tan(30) = 50 / (1/√3) = 50√3 meters

Correct Answer: A — 50√3

Q. A kite is flying at a height of 50 meters. If 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?

A. 25√3 meters
B. 50 meters
C. 50√3 meters
D. 75 meters

Solution

Distance = height / tan(angle) = 50 / (√3/3) = 50 * 3/√3 = 25√3 meters.

Correct Answer: A — 25√3 meters

Q. A kite is flying at a height of 60 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?

A. 60√3 meters
B. 30√3 meters
C. 20√3 meters
D. 10√3 meters

Solution

Distance = height / tan(angle) = 60 / (1/√3) = 60√3 meters.

Correct Answer: A — 60√3 meters

Q. A kite is flying at a height of 60 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?

A. 30 meters
B. 40 meters
C. 60 meters
D. 70 meters

Solution

Distance = height / tan(angle) = 60 / 1 = 60 meters.

Correct Answer: C — 60 meters

Q. A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 meters away from the wall, how high does the ladder reach on the wall?

A. 8 meters
B. 9 meters
C. 10 meters
D. 7 meters

Solution

Using Pythagoras: height = √(10^2 - 6^2) = √(100 - 36) = √64 = 8 meters.

Correct Answer: A — 8 meters

Q. A ladder 10 meters long reaches a window 8 meters above the ground. What is the angle of elevation of the ladder from the ground?

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

Solution

Using sin(θ) = opposite/hypotenuse, sin(θ) = 8/10, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Correct Answer: C — 60 degrees

Q. A ladder 10 meters long reaches a window 8 meters high. How far is the base of the ladder from the wall?

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

Solution

Using Pythagoras: base = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 meters

Correct Answer: A — 6 meters

Q. A ladder 10 meters long reaches a window 8 meters high. What is the angle of elevation of the ladder from the ground?

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

Solution

Using sin(θ) = opposite/hypotenuse, sin(θ) = 8/10, θ = arcsin(0.8) = 53.13 degrees.

Correct Answer: C — 60 degrees

Q. A ladder 20 meters long reaches a window 15 meters above the ground. What is the angle of elevation of the ladder from the ground?

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

Solution

Using sin(θ) = opposite/hypotenuse, sin(θ) = 15/20, θ = sin⁻¹(0.75) ≈ 48.6 degrees.

Correct Answer: C — 60 degrees

Q. A ladder 20 meters long reaches a window 16 meters above the ground. What is the angle of elevation of the ladder from the ground?

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

Solution

Using sin(θ) = opposite/hypotenuse, sin(θ) = 16/20, θ = sin⁻¹(0.8) ≈ 60 degrees.

Correct Answer: C — 60 degrees

Q. A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters away from the wall, how high does the ladder reach on the wall?

A. 24 meters
B. 20 meters
C. 21 meters
D. 22 meters

Solution

Using Pythagoras: height = √(25^2 - 7^2) = √(625 - 49) = √576 = 24 meters

Correct Answer: B — 20 meters

Q. A loan of $6000 is taken for 3 years at a bankers discount of 15%. What is the total discount?

A. $2700
B. $270
C. $600
D. $900

Solution

Total Discount = (6000 × 15 × 3) / 100 = $2700.

Correct Answer: A — $2700

Q. A man earns $1,200 per month. If he spends 75% of his income, how much does he save?

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

Solution

Spending = 75% of 1,200 = 900. Savings = 1,200 - 900 = 300.

Correct Answer: B — $300

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