Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. The average of 4 consecutive integers is 25. What is the largest of these integers?

A. 26
B. 27
C. 28
D. 29

Solution

Let the integers be x, x+1, x+2, x+3. Average = (4x + 6) / 4 = 25. Solving gives x = 24. Largest integer = x + 3 = 27.

Correct Answer: C — 28

Q. The average of 4 consecutive integers is 25. What is the smallest of these integers?

A. 23
B. 24
C. 25
D. 26

Solution

Let the integers be x, x+1, x+2, x+3. Average = (4x + 6) / 4 = 25. So, 4x + 6 = 100. Therefore, x = 23.

Correct Answer: A — 23

Q. The average of 4 numbers is 30. If one number is 10, what is the average of the other three numbers?

A. 28
B. 30
C. 32
D. 34

Solution

Total of 4 numbers = 4 * 30 = 120. Total of other three numbers = 120 - 10 = 110. Average of other three = 110 / 3 = 36.67, approximately 36.

Correct Answer: A — 28

Q. The average of 4 numbers is 30. If one number is increased by 10, what will be the new average?

A. 30
B. 32.5
C. 35
D. 37.5

Solution

Total = 30 * 4 = 120. New total = 120 + 10 = 130. New average = 130 / 4 = 32.5.

Correct Answer: B — 32.5

Q. The average of 5 numbers is 12. If one number is removed, the average becomes 10. What is the removed number?

A. 8
B. 10
C. 12
D. 14

Solution

Total of 5 numbers = 5 * 12 = 60. Total of 4 numbers = 4 * 10 = 40. Removed number = 60 - 40 = 20.

Correct Answer: D — 14

Q. The average of 5 numbers is 40. If the largest number is 60, what is the average of the other four numbers?

A. 35
B. 40
C. 45
D. 50

Solution

The total of the 5 numbers is 5 * 40 = 200. The sum of the other four numbers is 200 - 60 = 140. The average of the other four numbers is 140 / 4 = 35.

Correct Answer: A — 35

Q. The average of 8 numbers is 12. If one number is removed, the average becomes 10. What is the removed number?

A. 16
B. 18
C. 20
D. 22

Solution

The total of the 8 numbers is 8 * 12 = 96. The total of the remaining 7 numbers is 7 * 10 = 70. Therefore, the removed number is 96 - 70 = 26.

Correct Answer: C — 20

Q. The average of 8 numbers is 50. If one number is increased by 10, what will be the new average?

A. 50
B. 51
C. 52
D. 53

Solution

Total of 8 numbers = 8 * 50 = 400. New total = 400 + 10 = 410. New average = 410 / 8 = 51.25, approximately 51.

Correct Answer: B — 51

Q. The average of five numbers is 20. If one number is excluded, the average becomes 18. What is the excluded number?

A. 22
B. 20
C. 18
D. 16

Solution

Total of five numbers = 5 * 20 = 100. Total of four numbers = 4 * 18 = 72. Excluded number = 100 - 72 = 28.

Correct Answer: A — 22

Q. The average of three consecutive integers is 20. What is the largest of these integers?

A. 19
B. 20
C. 21
D. 22

Solution

Let the integers be x, x+1, x+2. Average = (x + (x+1) + (x+2)) / 3 = 20. Solving gives x = 19, largest integer = 21.

Correct Answer: C — 21

Q. The average of three numbers is 15. If one of the numbers is 12, what is the average of the other two numbers?

A. 14
B. 15
C. 16
D. 17

Solution

Total of three numbers = 3 * 15 = 45. Sum of other two numbers = 45 - 12 = 33. Average = 33 / 2 = 16.5.

Correct Answer: B — 15

Q. The average of three numbers is 20. If one number is 10, what is the average of the other two numbers?

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

Solution

Total of three numbers = 20 * 3 = 60. The sum of the other two = 60 - 10 = 50. Average = 50 / 2 = 25.

Correct Answer: A — 15

Q. The average of three numbers is 30. If one of the numbers is 10, what is the average of the other two numbers?

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

Solution

Let the three numbers be a, b, and c. We have (a + b + c) / 3 = 30. Thus, a + b + c = 90. If c = 10, then a + b = 90 - 10 = 80. The average of a and b is 80 / 2 = 40.

Correct Answer: A — 25

Q. The average of two numbers is 40. If one number is 30, what is the other number?

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

Solution

Let the other number be x. (30 + x) / 2 = 40. So, 30 + x = 80. Therefore, x = 50.

Correct Answer: A — 50

Q. The present age of a grandfather is 4 times that of his grandson. If the grandson is 5 years old, what is the grandfather's age?

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

Solution

If the grandson is 5 years old, then the grandfather is 4 * 5 = 20 years old.

Correct Answer: D — 30

Q. The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

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

Solution

Let the son's age be x. Then the father's age is x + 30. So, x + (x + 30) = 50. Solving gives x = 10.

Correct Answer: C — 20

Q. The sum of the ages of a father and his son is 50 years. If the father is 40 years old, how old is the son?

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

Solution

If the father is 40 years old, then the son is 50 - 40 = 10 years old.

Correct Answer: C — 20

Q. The sum of the ages of a mother and her daughter is 50 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 10
B. 8
C. 12
D. 6

Solution

Let the daughter's age be x. Then the mother's age is 4x. The equation is x + 4x = 50, which simplifies to 5x = 50, so x = 10.

Correct Answer: A — 10

Q. The sum of the ages of a mother and her daughter is 60 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 8
B. 10
C. 12
D. 15

Solution

Let the daughter's age be x. Then the mother's age is 4x. So, x + 4x = 60. Solving gives x = 12.

Correct Answer: B — 10

Q. Three pipes can fill a tank in 6, 8, and 12 hours respectively. If all three pipes are opened together, how long will it take to fill the tank?

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

Solution

The combined rate is 1/6 + 1/8 + 1/12 = 1/3. Therefore, it will take 3 hours to fill the tank.

Correct Answer: B — 3 hours

Q. Three years ago, a man was 5 times as old as his son. If the man is currently 38 years old, how old is his son now?

A. 6
B. 7
C. 8
D. 9

Solution

Let the son's age be x. Three years ago, the man was 35 and the son was x - 3. So, 35 = 5(x - 3). Solving gives x = 8.

Correct Answer: C — 8

Q. Three years ago, A was 2 times as old as B. If B is currently 12 years old, how old is A now?

A. 18
B. 20
C. 24
D. 30

Solution

Three years ago, B was 12 - 3 = 9 years old. A was 2 * 9 = 18 years old. Now, A is 18 + 3 = 21 years old.

Correct Answer: B — 20

Q. Three years ago, A was 5 times as old as B. If B is now 10 years old, how old is A now?

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

Solution

Three years ago, B was 7 years old. Therefore, A was 5 * 7 = 35 years old. Now, A is 35 + 3 = 38 years old.

Correct Answer: B — 30

Q. Three years ago, A was 5 times as old as B. If B is now 7 years old, how old is A now?

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

Solution

Three years ago, B was 4 years old. Therefore, A was 5 * 4 = 20 years old. Now, A is 20 + 3 = 23 years old.

Correct Answer: B — 30

Q. Three years ago, A was 5 times as old as B. If B is now 8 years old, how old is A now?

A. 28
B. 30
C. 25
D. 20

Solution

Three years ago, B was 5 years old. Therefore, A was 5 * 5 = 25 years old. Now, A is 25 + 3 = 28 years old.

Correct Answer: A — 28

Q. Three years ago, A was 5 years older than B. If B is now 12 years old, how old is A now?

A. 10
B. 12
C. 15
D. 18

Solution

Three years ago, B was 12 - 3 = 9 years old. A was 9 + 5 = 14 years old now.

Correct Answer: C — 15

Q. Two coins are tossed. What is the probability of getting at least one head?

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

Solution

The possible outcomes are HH, HT, TH, TT. The outcomes with at least one head are HH, HT, TH. So, the probability is 3/4.

Correct Answer: C — 3/4

Q. Two dice are rolled. What is the probability that the sum of the numbers on the dice is 7?

A. 1/6
B. 1/12
C. 1/36
D. 5/36

Solution

The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). There are 6 combinations out of 36 total outcomes, so the probability is 6/36 = 1/6.

Correct Answer: D — 5/36

Q. Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The combined rate is 1/12 + 1/18 = 5/36. Therefore, it will take 36/5 = 7.2 hours to fill the tank.

Correct Answer: C — 9 hours

Q. Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 6 hours
B. 7.5 hours
C. 8 hours
D. 9 hours

Solution

The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.

Correct Answer: B — 7.5 hours

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