Quantitative Apptitude - Average Online Test 2

Explanation
The average of 20 numbers is zero, which means that the sum of all these numbers is also zero. In order for the sum to be zero, it is possible for 19 numbers to be greater than zero, as long as the sum of the remaining numbers is negative and cancels out the positive values. Therefore, the maximum number of numbers that may be greater than zero is 19.

Explanation
The average speed of the train for the whole journey can be calculated by finding the harmonic mean of the speeds for the two legs of the journey. The time taken for the first leg of the journey (A to B) can be calculated by dividing the distance by the speed, which is 778 km / 84 km/h = 9.26 hours. The time taken for the second leg of the journey (B to A) can be calculated in the same way, which is 778 km / 56 km/h = 13.89 hours. The total time for the whole journey is the sum of these two times, which is 9.26 hours + 13.89 hours = 23.15 hours. The average speed is then calculated by dividing the total distance (2 * 778 km) by the total time (23.15 hours), which is 2 * 778 km / 23.15 hours = 67.2 km/h.

Explanation
The average age of the students is 9 years, which means that the sum of their ages is 9 times 30, or 270 years. When the teacher's age is included, the average becomes 10 years, so the sum of the ages is 10 times 31, or 310 years. To find the age of the teacher, we subtract the sum of the students' ages (270) from the sum of all ages (310), which gives us 40 years.

Explanation
To find the sale amount in the sixth month, we need to calculate the total sale for the 6 months. The average sale for 6 months should be Rs. 6500.

Total sale for 5 months = Rs. 6435 + Rs. 6927 + Rs. 6855 + Rs. 7230 + Rs. 6562 = Rs. 34009

To find the sale amount in the sixth month, we subtract the total sale for 5 months from the target average sale of 6 months multiplied by 6.

Target average sale for 6 months = Rs. 6500
Total sale for 6 months = Rs. 6500 * 6 = Rs. 39000

Sale amount in the sixth month = Total sale for 6 months - Total sale for 5 months
= Rs. 39000 - Rs. 34009
= Rs. 4991

Therefore, the sale amount in the sixth month must be Rs. 4991 to achieve an average sale of Rs. 6500.

Explanation
The average age for the whole class cannot be determined based on the given information. The question does not provide the number of boys and girls in the class, so it is not possible to calculate the overall average age. Therefore, the correct answer is "none of these".

Explanation
To find the run rate in the remaining 40 overs, we need to consider the total number of runs required and the number of overs remaining. The target is 282 runs, and the first 10 overs had a run rate of 3.2. This means that in the first 10 overs, 32 runs were scored. To reach the target of 282 runs, there are 40 overs remaining. Therefore, the remaining runs required are 282 - 32 = 250. The run rate needed in the remaining overs is the remaining runs divided by the remaining overs, which is 250/40 = 6.25.

Explanation
Three years ago, the average age of A, B, and C 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 B and C was 20 years. This means that the sum of their ages five years ago was 20 multiplied by 2, which is 40.
To find A's present age, we need to subtract the sum of B and C's ages five years ago from the sum of A, B, and C's ages three years ago.
81 - 40 = 41.
Since this is the age three years ago, we need to add 3 to get A's present age.
41 + 3 = 44.
Therefore, A's present age is 44.

Explanation
If the average of 20 numbers is zero, it means that the sum of all the numbers is also zero. In order for the sum to be zero, some numbers must be positive and some must be negative. However, the number of positive numbers cannot exceed the number of negative numbers, as that would result in a positive sum. Therefore, at most, there can be 19 numbers greater than zero, with one number being zero to balance out the sum.

Explanation
If the average age of 36 students is 14 years, then the total age of all the students is 36 * 14 = 504 years. When the teacher's age is included, the average increases by one, which means the total age of all the students and the teacher is now 505 years. Since the teacher's age is included, the teacher's age must be 505 - 504 = 1 year. Therefore, the teacher's age is 51 years.