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The average of seven consecutive odd numbers (in increasing order) is k. If the next four consecutive odd numbers are included, then the average of all the number is:
- a)k + 7
- b)k + 3
- c)k + 4
- d)k + 2
Correct answer is option 'C'. Can you explain this answer?
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The average of seven consecutive odd numbers (in increasing order) is ...
Given
The average of seven consecutive odd numbers (in increasing order) is k.
Let seven consecutive odd numbers be a, a + 2, a + 4, a + 6, a + 8, a + 10 and a + 12
Accordingly,
a + a + 2 + a + 4 + a + 6 + a + 8 + a + 10 + a + 12 = k × 7
⇒ 7a + 42 = 7k
⇒ a + 6 = k
⇒ a = k − 6
∴ New average = k - 6 + 10 = k + 4
Hence, the correct option is (C).
Most Upvoted Answer
The average of seven consecutive odd numbers (in increasing order) is ...
Problem:
The average of seven consecutive odd numbers (in increasing order) is k. If the next four consecutive odd numbers are included, then the average of all the numbers is:
a) k + 7
b) k + 3
c) k + 4
d) k + 2
Solution:
Let's assume the first odd number in the sequence is x.
So, the seven consecutive odd numbers would be x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12.
Finding the average of the seven consecutive odd numbers:
To find the average of these numbers, we need to sum them up and divide by the total count.
Sum of the numbers = x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12)
= 7x + (2 + 4 + 6 + 8 + 10 + 12)
= 7x + 42
Average of the numbers = (7x + 42) / 7 = x + 6
Given that the average of these seven numbers is k, we can write:
x + 6 = k
=> x = k - 6
Finding the average of all the numbers:
If we include the next four consecutive odd numbers, they would be x + 14, x + 16, x + 18, x + 20.
Now, the total count of numbers is 7 + 4 = 11.
To find the average, we need to sum up all the numbers and divide by the total count.
Sum of all the numbers = (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12 + x + 14 + x + 16 + x + 18 + x + 20)
= 11x + (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)
= 11x + 110
Average of all the numbers = (11x + 110) / 11 = x + 10
Substituting the value of x from the previous equation (x = k - 6), we get:
Average of all the numbers = (k - 6) + 10 = k + 4
Therefore, the average of all the numbers is k + 4, which corresponds to option c).
The average of seven consecutive odd numbers (in increasing order) is k. If the next four consecutive odd numbers are included, then the average of all the numbers is:
a) k + 7
b) k + 3
c) k + 4
d) k + 2
Solution:
Let's assume the first odd number in the sequence is x.
So, the seven consecutive odd numbers would be x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12.
Finding the average of the seven consecutive odd numbers:
To find the average of these numbers, we need to sum them up and divide by the total count.
Sum of the numbers = x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12)
= 7x + (2 + 4 + 6 + 8 + 10 + 12)
= 7x + 42
Average of the numbers = (7x + 42) / 7 = x + 6
Given that the average of these seven numbers is k, we can write:
x + 6 = k
=> x = k - 6
Finding the average of all the numbers:
If we include the next four consecutive odd numbers, they would be x + 14, x + 16, x + 18, x + 20.
Now, the total count of numbers is 7 + 4 = 11.
To find the average, we need to sum up all the numbers and divide by the total count.
Sum of all the numbers = (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12 + x + 14 + x + 16 + x + 18 + x + 20)
= 11x + (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)
= 11x + 110
Average of all the numbers = (11x + 110) / 11 = x + 10
Substituting the value of x from the previous equation (x = k - 6), we get:
Average of all the numbers = (k - 6) + 10 = k + 4
Therefore, the average of all the numbers is k + 4, which corresponds to option c).
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The average of seven consecutive odd numbers (in increasing order) is k. If the next four consecutive odd numbers are included, then the average of all the number is:a)k + 7b)k + 3c)k + 4d)k + 2Correct answer is option 'C'. Can you explain this answer?
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