Quantitative Aptitude for Competitive Exam Success

Quantitative Aptitude

Algebra Arithmetic Geometry & Mensuration Modern Math Number Systems

Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the circumference?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

The angle subtended at the circumference is half of that at the center, so it is 30 degrees.

Correct Answer: A — 30 degrees

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Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the remaining part of the circle?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

The angle subtended at the circumference is half of that at the center, so it is 30 degrees.

Correct Answer: A — 30 degrees

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Q. In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is the angle in radians subtended by the arc at the center? (2021)

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

Solution

The angle in radians is given by the formula θ = s/r, where s is the arc length. Thus, θ = 10/5 = 2 rad.

Correct Answer: B — 2 rad

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Q. In a circle, if the radius is doubled, how does the area change?

A. It remains the same.
B. It doubles.
C. It quadruples.
D. It increases by a factor of eight.

Solution

If the radius is doubled, the area increases by a factor of four (since area is proportional to the square of the radius).

Correct Answer: C — It quadruples.

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Q. In a circle, if the radius is increased by 50%, what happens to the area of the circle?

A. It increases by 50%
B. It doubles
C. It increases by 125%
D. It increases by 75%

Solution

If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.

Correct Answer: C — It increases by 125%

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Q. In a circle, if the radius is increased by 50%, what happens to the area?

A. Increases by 25%
B. Increases by 50%
C. Increases by 75%
D. Increases by 125%

Solution

If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.

Correct Answer: D — Increases by 125%

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Q. In a class of 30 students, 18 students study Mathematics, 15 study Science, and 10 study both subjects. How many students study only Mathematics?

A. 8
B. 10
C. 15
D. 18

Solution

To find the number of students who study only Mathematics, we use the formula: Only Mathematics = Total Mathematics - Both subjects. Thus, 18 - 10 = 8.

Correct Answer: A — 8

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Q. In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)

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

Solution

Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.

Correct Answer: B — 15

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Q. In a class of 30 students, the probability of a student being selected for a project is 0.4. What is the expected number of students selected?

A. 10
B. 12
C. 15
D. 20

Solution

The expected number of students selected is calculated as 30 * 0.4 = 12.

Correct Answer: B — 12

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Q. In a class of 40 students, 25 study English, 15 study Mathematics, and 10 study both. How many students study only English?

A. 15
B. 25
C. 10
D. 5

Solution

Students who study only English = Total English - Both = 25 - 10 = 15.

Correct Answer: A — 15

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Q. In a class of 40 students, 25 study English, 20 study Mathematics, and 10 study both. How many study only Mathematics?

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

Solution

To find the number of students who study only Mathematics, we subtract those who study both from those who study Mathematics: 20 - 10 = 10.

Correct Answer: B — 15

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Q. In a class of 40 students, 25% are girls. How many boys are there in the class?

A. 10
B. 15
C. 30
D. 20

Solution

Number of girls = 25% of 40 = 10. Number of boys = 40 - 10 = 30.

Correct Answer: C — 30

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Q. In a class of 50 students, 20 study English, 25 study Hindi, and 10 study both. How many students study only one language?

A. 35
B. 30
C. 25
D. 20

Solution

The number of students studying only one language is: (20 - 10) + (25 - 10) = 35.

Correct Answer: A — 35

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Q. In a class of 50 students, 20 study English, 25 study Hindi, and 10 study both. How many students study only Hindi?

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

Solution

To find the number of students who study only Hindi, we subtract those who study both from those who study Hindi: 25 - 10 = 15.

Correct Answer: A — 15

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Q. In a class of 50 students, 20 study English, 25 study History, and 10 study both. How many students study only History?

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

Solution

To find the number of students who study only History, we subtract those who study both from those who study History: 25 - 10 = 15.

Correct Answer: A — 15

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Q. In a class of 50 students, 20 study English, 25 study Mathematics, and 10 study both. How many students study only one subject?

A. 35
B. 25
C. 15
D. 45

Solution

The number of students studying only English is 20 - 10 = 10, and only Mathematics is 25 - 10 = 15. Thus, total studying only one subject is 10 + 15 = 25.

Correct Answer: A — 35

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Q. In a class of 50 students, 20 study History, 25 study Geography, and 10 study both. How many students study only Geography?

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

Solution

The number of students who study only Geography is 25 - 10 = 15.

Correct Answer: A — 15

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Q. In a class of 50 students, 20 study Mathematics, 25 study Science, and 10 study both. How many students study only Science?

A. 15
B. 25
C. 10
D. 5

Solution

The number of students who study only Science is 25 - 10 = 15.

Correct Answer: A — 15

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Q. In a class of 50 students, 25 study English, 20 study Hindi, and 5 study both. How many students study only one language?

A. 20
B. 25
C. 30
D. 35

Solution

The number of students studying only English is 25 - 5 = 20, and only Hindi is 20 - 5 = 15. Thus, total studying only one language is 20 + 15 = 35.

Correct Answer: D — 35

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Q. In a class of 50 students, 30 study English, 25 study Mathematics, and 10 study both. How many study only Mathematics?

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

Solution

Only Mathematics = Total Mathematics - Both = 25 - 10 = 15.

Correct Answer: A — 15

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Q. In a class of 50 students, 40% are girls. How many boys are there in the class? (2023)

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

Solution

Number of girls = 40% of 50 = 20. Therefore, number of boys = 50 - 20 = 30.

Correct Answer: B — 30

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Q. In a class of 60 students, 25 study History, 30 study Geography, and 10 study both. How many students study only Geography?

A. 20
B. 30
C. 10
D. 25

Solution

The number of students studying only Geography is 30 - 10 = 20.

Correct Answer: A — 20

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Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 10 and the number of girls is decreased by 5, what will be the new ratio of boys to girls? (2023)

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

Solution

Initially, there are 36 boys and 24 girls. After the changes, there will be 46 boys and 19 girls. The new ratio is 46:19, which simplifies to approximately 4:3.

Correct Answer: D — 4:3

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Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 5, what will be the new ratio of boys to girls? (2023)

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

Solution

Initially, there are 36 boys and 24 girls. After increasing boys by 5, there will be 41 boys and 24 girls, giving a new ratio of 41:24, which simplifies to approximately 4:3.

Correct Answer: A — 4:3

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Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 10, what will be the new ratio of boys to girls? (2023)

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

Solution

Initially, there are 36 boys and 24 girls. After increasing the boys by 10, there will be 46 boys and 24 girls, giving a new ratio of 46:24, which simplifies to 4:3.

Correct Answer: A — 4:3

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Q. In a class of 80 students, 50 like English, 30 like Hindi, and 10 like both. How many students like only Hindi?

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

Solution

The number of students who like only Hindi is 30 - 10 = 20.

Correct Answer: A — 20

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Q. In a class of 80 students, 50 like history, 30 like geography, and 10 like both. How many students like only geography?

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

Solution

The number of students who like only geography is 30 - 10 = 20.

Correct Answer: A — 20

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Q. In a class of 80 students, 50 study English, 40 study Hindi, and 20 study both. How many students study only Hindi?

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

Solution

The number of students studying only Hindi is 40 - 20 = 20.

Correct Answer: A — 20

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Q. In a class of students, the ratio of boys to girls is 3:2. If the total number of students is 50, how many boys are there? (2023)

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

Solution

Let the number of boys be 3x and girls be 2x. Then, 3x + 2x = 50, which gives x = 10. Therefore, boys = 3x = 30.

Correct Answer: B — 30

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Q. In a class, 12 students play cricket, 10 play football, and 5 play both. How many students play only cricket?

A. 5
B. 7
C. 10
D. 12

Solution

Only cricket players = Total cricket players - Both = 12 - 5 = 7.

Correct Answer: B — 7

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Quantitative Aptitude

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