Quantitative Apptitude - Average Online Test 7

Explanation
To find the average of all prime numbers between 30 and 50, we first need to identify the prime numbers within that range. The prime numbers between 30 and 50 are 31, 37, 41, 43, and 47. To calculate the average, we add these numbers together (31+37+41+43+47 = 199) and then divide by the total number of prime numbers (5). Therefore, the average of all prime numbers between 30 and 50 is 39.8.

Explanation
The question asks for the average of the first five multiples of 3. To find the average, we add up all the multiples of 3 and then divide the sum by the total number of multiples. The first five multiples of 3 are 3, 6, 9, 12, and 15. Adding these numbers gives us a sum of 45. Since there are five multiples, we divide the sum by 5 to get the average, which is 9.

Explanation
If the average weight of the class of 30 students is 40 kg and including the teacher's weight increases the average by 2 kg, then the total weight of the class without the teacher is 30 * 40 = 1200 kg.

When the teacher's weight is included, the new average becomes 40 + 2 = 42 kg.

To find the weight of the teacher, we subtract the total weight of the class without the teacher from the total weight of the class with the teacher: 1200 + x = 42 * 31, where x is the weight of the teacher.

Simplifying the equation, we get x = 42 * 31 - 1200 = 102 kg.

Therefore, the weight of the teacher is 102 kg.

Explanation
Let's assume the average age of the whole team is x. Since the captain is 26 years old and the wicket keeper is 3 years older, their combined age is 26 + 3 = 29. The remaining 9 players have an average age that is one year less than the average age of the whole team, which means their average age is x - 1. The total age of the remaining 9 players is (x - 1) * 9. Adding the ages of the captain and wicket keeper, we get (x - 1) * 9 + 29. This sum should be equal to the total age of the whole team, which is 11x. So, we have the equation (x - 1) * 9 + 29 = 11x. Solving this equation, we find x = 23, which is the average age of the team.

Explanation
The average of a set of numbers is found by adding up all the numbers in the set and then dividing the sum by the total number of values. In this case, the set of numbers is the first 40 natural numbers, which are 1, 2, 3, 4, ..., 40. To find the average, we add up all these numbers and divide the sum by 40. The sum of the first 40 natural numbers is 820. Dividing 820 by 40 gives us 20.5, which is the average of the first 40 natural numbers.

Explanation
To find the average of the first 20 multiples of 7, we need to add up all the multiples and then divide by 20. The first multiple of 7 is 7 itself, and the 20th multiple is 7 multiplied by 20, which equals 140. To find the sum of these multiples, we can use the formula for the sum of an arithmetic series: (n/2)(first term + last term), where n is the number of terms. Plugging in the values, we get (20/2)(7 + 140) = (10)(147) = 1470. Finally, we divide this sum by 20 to find the average, which is 1470/20 = 73.5.

Explanation
The arithmetic mean is calculated by summing all the numbers and dividing by the total number of values. In this case, the sum of the given numbers is 3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 = 137. Since there are 12 numbers in total, the mean is 137/12 = 11.4167. However, the student found the mean to be 12. To achieve a mean of 12, the number in the place of x must be 7, as it brings the sum to 137 + 7 = 144, and the mean becomes 144/12 = 12.

Explanation
Four years ago, the average age of Mr and Mrs Sharma was 28 years. This means that their combined age four years ago was 56 years (28 x 2).
If the present average age of Mr and Mrs Sharma and their son is 22 years, and assuming that the son was not born four years ago, we can subtract the combined age of Mr and Mrs Sharma (56 years) from the present average age (22 years) to find the age of their son.
22 - 56 = -34
Since a negative age is not possible, the son must be younger than four years old. Therefore, the age of their son is 2 years.

Explanation
Three years ago, the average age of the husband, wife, and child was 27 years. This means that the sum of their ages three years ago was 27 multiplied by 3, which is 81.
Five years ago, the average age of the wife and child was 20 years. This means that the sum of their ages five years ago was 20 multiplied by 2, which is 40.
To find the present age of the husband, we need to subtract the sum of the wife and child's ages five years ago (40) from the sum of their ages three years ago (81). This gives us 81 - 40 = 41.
Therefore, the present age of the husband is 41 years.

Explanation
The average of four consecutive even numbers is 27. Since the numbers are consecutive and even, they can be represented as x, x+2, x+4, and x+6. To find the largest number, we need to find the value of x+6. Since the average is 27, the sum of the four numbers is 27*4 = 108. Therefore, x + (x+2) + (x+4) + (x+6) = 108. Simplifying this equation, we get 4x + 12 = 108. Solving for x, we find x = 24. Therefore, the largest number is x+6 = 30.