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There is a sequence of 11 consecutive odd numbers. If the average of first 7 numbers is X, then find the average of all the 11 integers.
- a)X + 3
- b)X + 4
- c)X + 5
- d)X + 7
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Problem Analysis:
We are given a sequence of 11 consecutive odd numbers. Let's assume the first number in the sequence is 'a'. Therefore, the next 10 odd numbers will be 'a + 2', 'a + 4', 'a + 6', 'a + 8', 'a + 10', 'a + 12', 'a + 14', 'a + 16', 'a + 18', and 'a + 20'.
Calculating the Average of the First 7 Numbers:
To find the average of the first 7 numbers, we need to add them up and divide the sum by 7.
The sum of the first 7 numbers = (a) + (a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) + (a + 12) = 7a + 42
Average of the first 7 numbers = (7a + 42)/7 = a + 6 = X
Calculating the Average of all 11 Numbers:
To find the average of all 11 numbers, we need to add them up and divide the sum by 11.
The sum of all 11 numbers = (a) + (a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) + (a + 12) + (a + 14) + (a + 16) + (a + 18) + (a + 20) = 11a + 110
Average of all 11 numbers = (11a + 110)/11 = a + 10
Conclusion:
The average of the first 7 numbers is 'X', which is equal to 'a + 6'. Therefore, the average of all 11 numbers is 'a + 10'. Since 'a + 10' is equal to 'X + 4', the correct option is 'X 4' (option B).
Answer: X 4
We are given a sequence of 11 consecutive odd numbers. Let's assume the first number in the sequence is 'a'. Therefore, the next 10 odd numbers will be 'a + 2', 'a + 4', 'a + 6', 'a + 8', 'a + 10', 'a + 12', 'a + 14', 'a + 16', 'a + 18', and 'a + 20'.
Calculating the Average of the First 7 Numbers:
To find the average of the first 7 numbers, we need to add them up and divide the sum by 7.
The sum of the first 7 numbers = (a) + (a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) + (a + 12) = 7a + 42
Average of the first 7 numbers = (7a + 42)/7 = a + 6 = X
Calculating the Average of all 11 Numbers:
To find the average of all 11 numbers, we need to add them up and divide the sum by 11.
The sum of all 11 numbers = (a) + (a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) + (a + 12) + (a + 14) + (a + 16) + (a + 18) + (a + 20) = 11a + 110
Average of all 11 numbers = (11a + 110)/11 = a + 10
Conclusion:
The average of the first 7 numbers is 'X', which is equal to 'a + 6'. Therefore, the average of all 11 numbers is 'a + 10'. Since 'a + 10' is equal to 'X + 4', the correct option is 'X 4' (option B).
Answer: X 4
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