Quantitative Apptitude - Average Online Test 1

Explanation
When each number in a set is multiplied by the same constant, the average of the new set will also be multiplied by that constant. In this case, each number is multiplied by 12, so the average of the new set will be 7 * 12 = 84.

Explanation
To find the arithmetic mean, we add up all the numbers and divide by the total count. In this case, the sum of the given numbers is 3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 = 137. There are a total of 12 numbers given, including x. The mean is calculated as 137/12 = 11.42. However, the student found the mean to be 12. To achieve a mean of 12, the sum of the numbers should be 12 multiplied by 12, which is 144. Therefore, the number in place of x should be 144 - 137 = 7.

Explanation
Each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew. Since there are 2 nephews, the total amount received by the daughters and sons combined is 2 nephews x 4 times the amount received by each nephew + 5 sons x 5 times the amount received by each nephew = 8 times the amount received by each nephew + 25 times the amount received by each nephew = 33 times the amount received by each nephew. Therefore, the total amount received by the daughters and sons combined is 33 times the amount received by each nephew. The total amount divided among all the children is Rs. 8600, so each daughter receives Rs. 8600 / 33 = Rs. 260.

Explanation
In order to increase his average by 3 runs, the batsman must have scored a total of 3 x 17 = 51 runs in the 17th inning. Therefore, his average after the 17th inning would be (87 + 51) / 17 = 138 / 17 = 8.11, which is approximately equal to 39.

Explanation
The average of eight numbers is 14, which means that the sum of these eight numbers is 8 multiplied by 14, which is 112. The average of six of these numbers is 16, so the sum of these six numbers is 6 multiplied by 16, which is 96. To find the sum of the remaining two numbers, we subtract 96 from 112, which gives us 16. Since there are two numbers remaining, the average of these two numbers is 16 divided by 2, which is 8.

Explanation
The average weight of section A is 40 kg and there are 36 students in that section. Therefore, the total weight of section A is 40 kg * 36 = 1440 kg. Similarly, the average weight of section B is 35 kg and there are 44 students in that section. Therefore, the total weight of section B is 35 kg * 44 = 1540 kg. To find the average weight of the whole class, we need to calculate the total weight of the class, which is the sum of the weights of section A and section B. So, the total weight of the class is 1440 kg + 1540 kg = 2980 kg. Since there are a total of 36 + 44 = 80 students in the class, the average weight of the whole class is 2980 kg / 80 = 37.25 kg.

Explanation
If the average age of the class increases by 3 months when the age of the teacher is included, it means that the teacher's age is greater than the average age of the class. This implies that the teacher's age is greater than 15 years. Since the increase in average is only by 3 months, the teacher's age cannot be significantly higher than 15 years. Therefore, the closest option to 15 years is 25, which is the correct answer.

Explanation
David obtained marks in five subjects: English, Mathematics, Physics, Chemistry, and Biology. To find his average marks, we need to add up all the marks and divide by the number of subjects. Adding the marks, we get 76 + 65 + 82 + 67 + 85 = 375. Since there are five subjects, we divide 375 by 5 to get the average marks, which is 75.

Explanation
The average of the first four numbers is 25, which means their sum is 100. The average of the last three numbers is 35, so their sum is 105. To find the fourth number, we can subtract the sum of the first four numbers (100) from the sum of all six numbers (180). This gives us 80. Since the fourth number is the difference between the two sums, it must be 25.

Explanation
The average of 20 numbers is zero, which means that the sum of all the numbers is zero. In order for the sum to be zero, there must be an equal number of positive and negative numbers. Therefore, at most, only half of the numbers can be greater than zero. So, the correct answer is none of these options.