Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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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

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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

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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

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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

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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

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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

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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

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Q. A jogger runs at a speed of 8 km/h. How far can he run in 45 minutes?

A. 5 km
B. 6 km
C. 7 km
D. 4 km

Solution

Distance = Speed * Time = 8 km/h * (45/60) hours = 6 km.

Correct Answer: A — 5 km

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Q. A jogs at a speed of 8 km/h and B jogs at 10 km/h. If they start together, how far apart will they be after 30 minutes?

A. 2 km
B. 1 km
C. 1.5 km
D. 3 km

Solution

Distance covered by A in 0.5 hours = 8 km/h * 0.5 = 4 km. Distance covered by B = 10 km/h * 0.5 = 5 km. Difference = 5 km - 4 km = 1 km.

Correct Answer: A — 2 km

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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

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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

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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

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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

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Q. A kite is flying at a height of 40 meters. If the string makes an angle of 60 degrees with the ground, how long is the string?

A. 20√3 meters
B. 40 meters
C. 80 meters
D. 60 meters

Solution

Length of string = height / sin(60) = 40 / (√3/2) = 80/√3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Q. A ladder is leaning against a wall. If the foot of the ladder is 6 meters away from the wall and the top of the ladder reaches a height of 8 meters, what is the length of the ladder?

A. 10 meters
B. 12 meters
C. 14 meters
D. 16 meters

Solution

Using the Pythagorean theorem, length of ladder = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 meters.

Correct Answer: A — 10 meters

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Q. A ladder leans against a wall making an angle of 60 degrees with the ground. If the foot of the ladder is 5 meters away from the wall, what is the height of the ladder on the wall?

A. 5√3 meters
B. 10 meters
C. 5 meters
D. 10√3 meters

Solution

Height = 5 * √3 = 5√3 meters.

Correct Answer: A — 5√3 meters

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Q. A laptop is sold for $800 after a discount of 20%. What was the marked price?

A. $1000
B. $960
C. $800
D. $850

Solution

Let Marked Price = x. Selling Price = x - 20% of x = 0.8x. 0.8x = 800. x = 800/0.8 = 1000.

Correct Answer: A — $1000

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Q. A laptop is sold for $900 after a profit of 25%. What was the cost price?

A. $700
B. $750
C. $800
D. $850

Solution

Let Cost Price = x. Selling Price = x + 25% of x = 1.25x. 1.25x = 900. x = 900/1.25 = 720.

Correct Answer: B — $750

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Arithmetic Aptitude

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