Question:
If the average of four consecutive even numbers is 31, then find the smallest and the greatest numbers among the given even numbers.
Correct Answer
28 and 34
Solution And Explanation
Solution
Given, the average of four consecutive even numbers = 31
Thus, the smallest and the greatest number among the given four even numbers = ?
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
Now,
Formula to find the
Average = Sum of observations/Numbers of observations
Therefore, the average of the given four consecutive even numbers
= Sum of the four consecutive even numbers/4
⇒ 31 = x+(x+2)+(x+4)+(x+6)/4
⇒ 31 = x+x+2+x+4+x+6/4
⇒ 31 = 4x + 12/4
After taking 4 as common from the numerator
⇒ 31 = 4 (x + 3)/ 4
⇒ 31 = x + 3
⇒ x + 3 = 31
After transposing 3 to RHS
⇒ x = 31 – 3
⇒ x = 28
Thus, first and the smallest even number = 28
And, the 4th and the greatest even number = x + 6
= 28 + 6 = 34
∴ The 4th and the greatest even number = 34
Therefore, the smallest and the greatest even numbers among the given consecutive four even numbers = 28 and 34 Answer
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.
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