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The average of four consecutive odd numbers is 64. What is the value of the largest number?
- a)65
- b)69
- c)71
- d)67
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The average of four consecutive odd numbers is 64. What is the value ...
To find the value of the largest number in a set of four consecutive odd numbers, we can use the concept of averages.
Step 1: Setting up the problem
Let's assume that the first odd number in the set is 'x'. Since the numbers are consecutive, the next three odd numbers will be 'x+2', 'x+4', and 'x+6'.
Step 2: Finding the average
The average of these four numbers can be calculated by summing up all the numbers and dividing the sum by the total number of terms. In this case, we have:
Average = (x + (x+2) + (x+4) + (x+6))/4
Simplifying the equation:
Average = (4x + 12)/4
Step 3: Solving the equation
According to the problem, the average of these four numbers is 64. So we can write the equation as:
64 = (4x + 12)/4
To remove the fraction, we can multiply both sides of the equation by 4:
256 = 4x + 12
Subtracting 12 from both sides:
244 = 4x
Finally, dividing both sides by 4:
61 = x
Step 4: Finding the largest number
Now that we have the value of the first odd number, which is 61, we can find the value of the largest number in the set by adding 6 to it:
Largest number = x + 6 = 61 + 6 = 67
Therefore, the value of the largest number in the set of four consecutive odd numbers is 67.
Hence, the correct answer is option D) 67.
Step 1: Setting up the problem
Let's assume that the first odd number in the set is 'x'. Since the numbers are consecutive, the next three odd numbers will be 'x+2', 'x+4', and 'x+6'.
Step 2: Finding the average
The average of these four numbers can be calculated by summing up all the numbers and dividing the sum by the total number of terms. In this case, we have:
Average = (x + (x+2) + (x+4) + (x+6))/4
Simplifying the equation:
Average = (4x + 12)/4
Step 3: Solving the equation
According to the problem, the average of these four numbers is 64. So we can write the equation as:
64 = (4x + 12)/4
To remove the fraction, we can multiply both sides of the equation by 4:
256 = 4x + 12
Subtracting 12 from both sides:
244 = 4x
Finally, dividing both sides by 4:
61 = x
Step 4: Finding the largest number
Now that we have the value of the first odd number, which is 61, we can find the value of the largest number in the set by adding 6 to it:
Largest number = x + 6 = 61 + 6 = 67
Therefore, the value of the largest number in the set of four consecutive odd numbers is 67.
Hence, the correct answer is option D) 67.
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Community Answer
The average of four consecutive odd numbers is 64. What is the value ...
Short trick: 61, 63,64, 65, 67 ( write two consecutive odd number after 64 and two consecutive odd number before 64)
So, larger number =67
Let the consecutive odd numbers x+1,x+3,x+5,x+7
sum = x+1+x+3+x+5+x+7
sum = 4x+16
we know
sum = average x no of terms
4x+16=64×4
4x+16=256
4x=240
x=60
required number = 60+7
required number = 67
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The average of four consecutive odd numbers is 64. What is the value of the largest number?a)65b)69c)71d)67Correct answer is option 'D'. Can you explain this answer?
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