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The average of 6 consecutive even numbers is 25. If the next even number is also considered, then what is the new average?
- a)27
- b)25
- c)26
- d)28
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The average of 6 consecutive even numbers is 25. If the next even numb...
Let the first integer be 2x.
Average of 6 consecutive integers: (2x + (2x + 2) + ... + (2x + 10))/6= 12x + 2(1 + 2 + ... + 5) = 12x + 30 = 25 × 6 = 150
⇒ x = 10.
Average of new numbers: (2x + (2x + 2) + ... + (2x + 12) )/ 7 = (14x + 42)/7 = 2x + 6 = 20 + 6 = 26.
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The average of 6 consecutive even numbers is 25. If the next even numb...
Calculation of the New Average
To find the new average after considering the next even number, we first need to determine the 6 consecutive even numbers.
Step 1: Finding the 6 Consecutive Even Numbers
Let's assume the first even number is x. The next 5 even numbers will be x+2, x+4, x+6, x+8, and x+10.
Since the average of these 6 numbers is 25, we can set up an equation:
(x + x+2 + x+4 + x+6 + x+8 + x+10) / 6 = 25
Simplifying the equation:
(6x + 30) / 6 = 25
6x + 30 = 150
6x = 120
x = 20
So, the consecutive even numbers are 20, 22, 24, 26, 28, and 30.
Step 2: Calculating the New Average
Now, we need to include the next even number after 30, which is 32, to find the new average.
Adding 32 to the previous sum of 150:
150 + 32 = 182
Since we now have 7 numbers, we divide the sum by 7 to get the new average:
182 / 7 = 26
Therefore, the new average after considering the next even number is 26. Hence, the correct answer is option 'c) 26'.
To find the new average after considering the next even number, we first need to determine the 6 consecutive even numbers.
Step 1: Finding the 6 Consecutive Even Numbers
Let's assume the first even number is x. The next 5 even numbers will be x+2, x+4, x+6, x+8, and x+10.
Since the average of these 6 numbers is 25, we can set up an equation:
(x + x+2 + x+4 + x+6 + x+8 + x+10) / 6 = 25
Simplifying the equation:
(6x + 30) / 6 = 25
6x + 30 = 150
6x = 120
x = 20
So, the consecutive even numbers are 20, 22, 24, 26, 28, and 30.
Step 2: Calculating the New Average
Now, we need to include the next even number after 30, which is 32, to find the new average.
Adding 32 to the previous sum of 150:
150 + 32 = 182
Since we now have 7 numbers, we divide the sum by 7 to get the new average:
182 / 7 = 26
Therefore, the new average after considering the next even number is 26. Hence, the correct answer is option 'c) 26'.
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The average of 6 consecutive even numbers is 25. If the next even number is also considered, then what is the new average?a)27b)25c)26d)28Correct answer is option 'C'. Can you explain this answer?
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The average of 6 consecutive even numbers is 25. If the next even number is also considered, then what is the new average?a)27b)25c)26d)28Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The average of 6 consecutive even numbers is 25. If the next even number is also considered, then what is the new average?a)27b)25c)26d)28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average of 6 consecutive even numbers is 25. If the next even number is also considered, then what is the new average?a)27b)25c)26d)28Correct answer is option 'C'. Can you explain this answer?.
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