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If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.
- a)68
- b)70
- c)50
- d)21
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the average of five consecutive even numbers is 66, then find the a...
GIVEN:
Average of five consecutive even numbers = 66
Average of five consecutive even numbers = 66
FORMULA USED:
Required Average = sum of the series / 7
Required Average = sum of the series / 7
CALCULATION:
Let the first five integer are (a + 2), (a + 4), (a + 6), (a + 8) and (a + 10)
Let the first five integer are (a + 2), (a + 4), (a + 6), (a + 8) and (a + 10)
Now
(a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) = 66 × 5
⇒ 5a + 30 = 330
⇒ 5a = 300
⇒ a = 60
So, the series is 62, 64, 66, 68, 70, 72 and 74.
Required average
⇒ (62 + 64 + 66 + 68 + 70 + 72 + 74)/7 = 68
(a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) = 66 × 5
⇒ 5a + 30 = 330
⇒ 5a = 300
⇒ a = 60
So, the series is 62, 64, 66, 68, 70, 72 and 74.
Required average
⇒ (62 + 64 + 66 + 68 + 70 + 72 + 74)/7 = 68
Most Upvoted Answer
If the average of five consecutive even numbers is 66, then find the a...
GIVEN:
Average of five consecutive even numbers = 66
Average of five consecutive even numbers = 66
FORMULA USED:
Required Average = sum of the series / 7
Required Average = sum of the series / 7
CALCULATION:
Let the first five integer are (a + 2), (a + 4), (a + 6), (a + 8) and (a + 10)
Let the first five integer are (a + 2), (a + 4), (a + 6), (a + 8) and (a + 10)
Now
(a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) = 66 × 5
⇒ 5a + 30 = 330
⇒ 5a = 300
⇒ a = 60
So, the series is 62, 64, 66, 68, 70, 72 and 74.
Required average
⇒ (62 + 64 + 66 + 68 + 70 + 72 + 74)/7 = 68
(a + 2) + (a + 4) + (a + 6) + (a + 8) + (a + 10) = 66 × 5
⇒ 5a + 30 = 330
⇒ 5a = 300
⇒ a = 60
So, the series is 62, 64, 66, 68, 70, 72 and 74.
Required average
⇒ (62 + 64 + 66 + 68 + 70 + 72 + 74)/7 = 68
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Community Answer
If the average of five consecutive even numbers is 66, then find the a...
Problem:
If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even numbers of the same five consecutive even number series.
Solution:
To solve this problem, we need to understand the concept of consecutive even numbers and how to find their average. Let's break down the solution into smaller steps.
Step 1: Understanding the given information
We are given that the average of five consecutive even numbers is 66. This means that if we have five consecutive even numbers, their average will be 66. Let's assume the first number in this series is 'x'. Therefore, the five consecutive even numbers will be x, x+2, x+4, x+6, and x+8.
Step 2: Finding the average of the first 7 consecutive even numbers
Now, we need to find the average of the first 7 consecutive even numbers of the same series. Let's assume the first number of this series is 'y'. Therefore, the seven consecutive even numbers will be y, y+2, y+4, y+6, y+8, y+10, and y+12.
Step 3: Relating the two series
Since we are given that the average of the first series is 66, we can write the following equation:
(x + (x+2) + (x+4) + (x+6) + (x+8)) / 5 = 66
Similarly, to find the average of the second series, we can write:
(y + (y+2) + (y+4) + (y+6) + (y+8) + (y+10) + (y+12)) / 7 = ?
Step 4: Solving the equation
Let's solve the first equation to find the value of 'x':
(5x + 20) / 5 = 66
5x + 20 = 330
5x = 310
x = 62
Now, substitute the value of 'x' in the second equation and solve for the average of the second series:
(y + (y+2) + (y+4) + (y+6) + (y+8) + (y+10) + (y+12)) / 7 = ?
(7y + 42) / 7 = ?
7y + 42 = ?
7y = ?
y = ?
Step 5: Finding the answer
To find the average of the second series, we need to find the value of 'y'. However, we can see that the value of 'y' is not determined by the given information. Therefore, we cannot find the exact average of the second series. However, we can make an estimation.
Since both series have the same difference between consecutive numbers (2), we can assume that the average of the second series will also be close to 66. Therefore, the closest option to 66 is option A, which is 68. Hence, the answer is option A.
Answer: Option A (68)
If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even numbers of the same five consecutive even number series.
Solution:
To solve this problem, we need to understand the concept of consecutive even numbers and how to find their average. Let's break down the solution into smaller steps.
Step 1: Understanding the given information
We are given that the average of five consecutive even numbers is 66. This means that if we have five consecutive even numbers, their average will be 66. Let's assume the first number in this series is 'x'. Therefore, the five consecutive even numbers will be x, x+2, x+4, x+6, and x+8.
Step 2: Finding the average of the first 7 consecutive even numbers
Now, we need to find the average of the first 7 consecutive even numbers of the same series. Let's assume the first number of this series is 'y'. Therefore, the seven consecutive even numbers will be y, y+2, y+4, y+6, y+8, y+10, and y+12.
Step 3: Relating the two series
Since we are given that the average of the first series is 66, we can write the following equation:
(x + (x+2) + (x+4) + (x+6) + (x+8)) / 5 = 66
Similarly, to find the average of the second series, we can write:
(y + (y+2) + (y+4) + (y+6) + (y+8) + (y+10) + (y+12)) / 7 = ?
Step 4: Solving the equation
Let's solve the first equation to find the value of 'x':
(5x + 20) / 5 = 66
5x + 20 = 330
5x = 310
x = 62
Now, substitute the value of 'x' in the second equation and solve for the average of the second series:
(y + (y+2) + (y+4) + (y+6) + (y+8) + (y+10) + (y+12)) / 7 = ?
(7y + 42) / 7 = ?
7y + 42 = ?
7y = ?
y = ?
Step 5: Finding the answer
To find the average of the second series, we need to find the value of 'y'. However, we can see that the value of 'y' is not determined by the given information. Therefore, we cannot find the exact average of the second series. However, we can make an estimation.
Since both series have the same difference between consecutive numbers (2), we can assume that the average of the second series will also be close to 66. Therefore, the closest option to 66 is option A, which is 68. Hence, the answer is option A.
Answer: Option A (68)
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If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer?
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If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer?.
If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the average of five consecutive even numbers is 66, then find the average of the first 7 consecutive even number of the same five consecutive even number series.a)68b)70c)50d)21Correct answer is option 'A'. Can you explain this answer?.
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