For any symmetric sequence, the sum of the highest and lowest is twice the average. Thus, 2 * 15 = 30. (The numbers are 11, 13, 15, 17, 19. 11+19 = 30).
7522
In a class, the average age of all the boys is 15 years, and that of the girls is 12 years. If the ratio of boys to girls is 3:2, find the average age of the entire class.
Let the number of boys be 3k and girls be 2k. Total age of boys = 3k * 15 = 45k. Total age of girls = 2k * 12 = 24k. Total age = 69k. Total students = 5k. Average = 69k / 5k = 13.8 years.
7523
The average of x numbers is 3x. If x-1 is subtracted from each number, the new average will be:
The first 10 whole numbers are 0, 1, 2, ..., 9. Their sum is 9*10/2 = 45. Average = 45 / 10 = 4.5.
7525
A student's average marks in 5 subjects is 80. If the marks of one subject are excluded, the average drops to 78. What were the marks of the excluded subject?
The average of an arithmetic progression increases by half the total common difference added. Adding 5 new even numbers shifts the midpoint by 5 positions (each representing half a step between elements). The new average is M + 5.
7528
Average of 5 numbers is 20. If each number is multiplied by 2 and then 5 is added to each, the new average will be:
When operations are uniformly applied to all elements, they apply to the average. Multiply average by 2: 20 * 2 = 40. Then add 5: 40 + 5 = 45.
7529
The average age of a class of 40 students is 18 years. When the teacher's age is included, the average increases by 0.5 years. What is the teacher's age?
Total age initially = 40 * 18 = 720. With teacher, total people = 41. New average = 18.5. New total age = 41 * 18.5 = 758.5. Teacher's age = 758.5 - 720 = 38.5 years.
7530
The average temperature of the first 4 days of a week is 37°C and that of the last 4 days is 41°C. If the average temperature of the whole week is 39°C, the temperature of the fourth day is:
Sum of first 4 days = 4 * 37 = 148. Sum of last 4 days = 4 * 41 = 164. Sum of all 7 days = 7 * 39 = 273. The fourth day is counted twice in the first and last sums. Temp of 4th day = (148 + 164) - 273 = 312 - 273 = 39°C.
