If the average of the first four of five numbers in decreasing order is 25 and the average of the last four numbers is 20, then what is the difference between the first and the last number?

examrobotsa's picture

Submitted by examrobotsa on

Q: 34 (CAPF/2022)
If the average of the first four of five numbers in decreasing order is 25 and the average of the last four numbers is 20, then what is the difference between the first and the last number?

question_subject: 

Maths

question_exam: 

CAPF

stats: 

0,7,5,1,2,2,7

Explanation:

To solve this problem, we must first take into consideration that the average of a set of numbers is calculated by adding them up and dividing by the quantity of numbers.

In the first instance, the average of the first four of five numbers is given as 25. This means their total sum is 100 (25*4). In the second instance, the average of the last four out of the five numbers is 20, meaning their total sum is 80(20*4).

Since both sets overlap by including three numbers, we know that the sum of these three numbers is the same in both sets. Therefore, by subtracting the second sum (80) from the first (100), we can find the difference between the first and the last number, which is 20.

So, the correct answer should be option 4.