Question : If the average of five consecutive even numbers is 24, the find the smallest and the greatest numbers.
Correct Answer 20 and 28
Solution & Explanation
Solution
Before going further, it is necessary to know some of the important terms used in the given question
Some Important Terms Used in the given Question
Consecutive Numbers: Numbers in continuation are called Consecutive Numbers, for example: 1, 2, 3, 4, . . . etc.
Even Number:
Numbers that can be divided exactly by 2, i.e. leaving no remainder after dividing by 2, are known as Even Numbers
Consecutive Even Numbers:
Even numbers in continuation are called Consecutive Even Numbers, such as 2, 4, 6, 8, . . . . etc.
How to get next consecutive even numbers to the given even number
Here, it can be observed easily, that there is a difference of 2 between two consecutive even numbers. This means the next consecutive even number can be obtained by the addition of 2 in an even number.
Example:
If 2 is the first even number, then second consecutive even number to 2
= 2 + 2 = 4
Similarly, the third consecutive even number to 2
= 2 + 2 + 2 = 2 + 4 = 6
And, the fourth consecutive even number to 2
= 2 + 2 + 2 + 2 = 2 + 6 = 8 and so on.
In short, next consecutive even number can be obtained by adding 2 in an even number.
Now, Solution of the given Question
Let first even number = x.
Therefore, the second consecutive even number = x + 2
And, the third consecutive even number = x + 4
And, the fourth consecutive even number = x + 6
And, the fifth consecutive even number = x + 8
Now, the formu
Formula to find the
Average = Sum of observations/Numbers of observations
Therefore, the average of the given five consecutive even numbers
= The sum of the five consecutive even numbers/5
⇒ 24 = x+(x+2)+(x+4)+(x+6)+(x+8)/5
⇒ 24 = x+x+2+x+4+x+6+x+8/5
⇒ 24 = 5x + 20/5
After taking 5 as common from the numerator
⇒ 24 = 5 (x + 4)/ 5
⇒ 24 = x + 24
⇒ x + 4 = 24
After transposing 4 to RHS
⇒ x = 24 – 4
⇒ x = 20
Thus, first and the smallest even number = 20
And, the 5th and the greatest even number = x + 8
= 20 + 8 = 28
∴ The 5th and the greatest even number = 28
Therefore, the smallest and the greatest even numbers among the given consecutive five even numbers = 20 and 28 Answer
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