Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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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

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

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

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

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

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

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

Q. In a mixture of 50 liters, the ratio of milk to water is 3:2. How many liters of milk are there?

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

Solution

In a 3:2 ratio, total parts = 3 + 2 = 5. Milk = (3/5) * 50 = 30 liters.

Correct Answer: C — 30 liters

Q. In a mixture of 90 liters, the ratio of vinegar to water is 1:4. How many liters of vinegar are there?

A. 18 liters
B. 20 liters
C. 15 liters
D. 12 liters

Solution

Vinegar = (1/5) * 90 = 18 liters.

Correct Answer: A — 18 liters

Q. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours and then increases his speed to 15 km/h for the next 3 hours, what is his average speed for the entire race?

A. 12
B. 13
C. 14
D. 15

Solution

Total distance = (10 * 2) + (15 * 3) = 20 + 45 = 65 km. Total time = 2 + 3 = 5 hours. Average speed = 65 / 5 = 13 km/h.

Correct Answer: B — 13

Q. In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

A. 60
B. 40
C. 20
D. 30

Solution

The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 4 is C(4, 2). Total = C(5, 2) * C(4, 2) = 10 * 6 = 60.

Correct Answer: A — 60

Q. In how many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

A. 100
B. 120
C. 150
D. 200

Solution

The number of ways is C(5,2) * C(6,3) = 10 * 20 = 200.

Correct Answer: B — 120

Q. In how many ways can 2 out of 5 different fruits be selected?

A. 10
B. 15
C. 20
D. 5

Solution

The number of ways to choose 2 fruits from 5 is C(5, 2) = 10.

Correct Answer: A — 10

Q. In how many ways can 3 different prizes be awarded to 5 students?

A. 60
B. 100
C. 30
D. 20

Solution

The number of ways to award 3 different prizes to 5 students is P(5, 3) = 5! / (5-3)! = 60.

Correct Answer: A — 60

Q. In how many ways can 3 different trophies be awarded to 10 students?

A. 720
B. 1000
C. 120
D. 300

Solution

The number of ways to award 3 trophies to 10 students is 10P3 = 720.

Correct Answer: A — 720

Q. In how many ways can 3 students be selected from a group of 10?

A. 120
B. 90
C. 100
D. 80

Solution

The number of ways to choose 3 students from 10 is C(10, 3) = 120.

Correct Answer: A — 120

Q. In how many ways can 4 different colored balls be arranged in a row?

A. 16
B. 24
C. 32
D. 48

Solution

The number of arrangements is 4! = 24.

Correct Answer: B — 24

Q. In how many ways can 4 different prizes be awarded to 10 students?

A. 5040
B. 720
C. 100
D. 40

Solution

The number of ways to award 4 different prizes to 10 students is P(10, 4) = 10! / (10-4)! = 5040.

Correct Answer: A — 5040

Q. In how many ways can 4 people be seated at a round table?

A. 24
B. 12
C. 6
D. 4

Solution

The number of arrangements of 4 people at a round table is (4-1)! = 6.

Correct Answer: B — 12

Q. In how many ways can 5 books be arranged on a shelf?

A. 120
B. 60
C. 24
D. 30

Solution

The number of ways to arrange 5 books is 5! = 120.

Correct Answer: A — 120

Q. In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?

A. 48
B. 120
C. 60
D. 24

Solution

Treat the 2 specific books as one unit. Then, we have 4 units to arrange: 4! × 2! = 48.

Correct Answer: A — 48

Q. In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be placed?

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

Solution

The number of ways to select and arrange 3 books from 5 is P(5, 3) = 5! / (5-3)! = 60.

Correct Answer: B — 120

Q. In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be displayed at a time?

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

Solution

The number of ways to select and arrange 3 books from 5 is 5P3 = 60.

Correct Answer: A — 60

Q. In how many ways can 5 different prizes be distributed among 3 students?

A. 243
B. 125
C. 60
D. 30

Solution

The number of ways to distribute 5 different prizes among 3 students is 3^5 = 243.

Correct Answer: A — 243

Q. In how many ways can 5 different trophies be awarded to 3 students?

A. 60
B. 100
C. 30
D. 20

Solution

The number of ways to award 5 trophies to 3 students is 3^5 = 243.

Correct Answer: A — 60

Q. In how many ways can 6 different books be arranged on a shelf if 2 specific books must be together?

A. 120
B. 720
C. 240
D. 60

Solution

Treat the 2 specific books as one unit. Then, we have 5 units to arrange: 5! = 120. The 2 books can be arranged in 2! = 2 ways. Total = 120 * 2 = 240.

Correct Answer: B — 720

Q. In how many ways can 6 people be seated around a circular table?

A. 720
B. 120
C. 60
D. 30

Solution

The number of ways to arrange 6 people around a circular table is (6-1)! = 5! = 120.

Correct Answer: B — 120

Q. In how many ways can 6 people be seated at a round table?

A. 120
B. 720
C. 60
D. 30

Solution

The number of ways to arrange 6 people at a round table is (6-1)! = 5! = 120.

Correct Answer: A — 120

Q. In how many ways can 6 people be seated in a round table?

A. 720
B. 120
C. 60
D. 30

Solution

The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.

Correct Answer: A — 720

Q. In how many ways can 7 different books be arranged if 3 specific books must be on the top?

A. 720
B. 120
C. 5040
D. 840

Solution

The 3 specific books can be arranged in 3! = 6 ways. The remaining 4 books can be arranged in 4! = 24 ways. Total = 6 * 24 = 144.

Correct Answer: A — 720

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