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 & 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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