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Average of 7 consecutive odd numbers is 31. If the previous and next odd number to these 7 odd numbers are also included, then what will be the new average?
- a)33
- b)31
- c)35
- d)29
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Average of 7 consecutive odd numbers is 31. If the previous and next o...
Let 7 odd consecutive numbers are (n - 6), (n - 4), (n - 2), n, (n + 1), (n + 4), (n + 6)
Given that, Average = 31
Average = middle term = n = 31
If we add previous and next odd number to these 7 odd numbers, again middle term will be
n = 31
∴ New average = 31
Most Upvoted Answer
Average of 7 consecutive odd numbers is 31. If the previous and next o...
To find the average of 7 consecutive odd numbers, we need to determine the middle number first.
Let's assume the middle number is 'x'. Since there are 7 consecutive odd numbers, the other 6 numbers can be represented as (x-2), (x-4), (x-6), (x+2), (x+4), and (x+6).
The average of these 7 numbers can be calculated by adding them all together and then dividing by 7:
Average = (x + (x-2) + (x-4) + (x-6) + (x+2) + (x+4) + (x+6)) / 7
According to the given information, the average is 31. So we can set up the equation:
31 = (x + (x-2) + (x-4) + (x-6) + (x+2) + (x+4) + (x+6)) / 7
Now let's simplify the equation:
31 = (7x) / 7
31 = x
So the middle number is 31.
To find the new average when the previous and next odd numbers are included, we need to add 2 more numbers to the series. These numbers can be represented as (x-8) and (x+8).
Now we have a total of 9 odd numbers: (x-8), (x-6), (x-4), (x-2), x, (x+2), (x+4), (x+6), and (x+8).
To find the new average, we add up all these numbers and divide by 9:
New Average = ((x-8) + (x-6) + (x-4) + (x-2) + x + (x+2) + (x+4) + (x+6) + (x+8)) / 9
Simplifying the equation:
New Average = (9x) / 9
New Average = x
Since we found earlier that x = 31, the new average is also 31.
Therefore, the correct answer is option B) 31.
Let's assume the middle number is 'x'. Since there are 7 consecutive odd numbers, the other 6 numbers can be represented as (x-2), (x-4), (x-6), (x+2), (x+4), and (x+6).
The average of these 7 numbers can be calculated by adding them all together and then dividing by 7:
Average = (x + (x-2) + (x-4) + (x-6) + (x+2) + (x+4) + (x+6)) / 7
According to the given information, the average is 31. So we can set up the equation:
31 = (x + (x-2) + (x-4) + (x-6) + (x+2) + (x+4) + (x+6)) / 7
Now let's simplify the equation:
31 = (7x) / 7
31 = x
So the middle number is 31.
To find the new average when the previous and next odd numbers are included, we need to add 2 more numbers to the series. These numbers can be represented as (x-8) and (x+8).
Now we have a total of 9 odd numbers: (x-8), (x-6), (x-4), (x-2), x, (x+2), (x+4), (x+6), and (x+8).
To find the new average, we add up all these numbers and divide by 9:
New Average = ((x-8) + (x-6) + (x-4) + (x-2) + x + (x+2) + (x+4) + (x+6) + (x+8)) / 9
Simplifying the equation:
New Average = (9x) / 9
New Average = x
Since we found earlier that x = 31, the new average is also 31.
Therefore, the correct answer is option B) 31.
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Average of 7 consecutive odd numbers is 31. If the previous and next odd number to these 7 odd numbers are also included, then what will be the new average?a)33b)31c)35d)29Correct answer is option 'B'. Can you explain this answer?
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