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The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?
- a)125
- b)144
- c)158
- d)163
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The sum of eight consecutive odd numbers is 656. The average of four c...
The sum of 8 consecutive odd numbers is 656
⇒ Average of the 8 odd numbers = 656/8 = 82
the odd numbers immediately preceding and succeeding 82 are 81 are 83 respectively and these will be the middle numbers.
Therefore, we see that 4th and 5th odd numbers are 81 and 83 respectively.
Thus we can easily obtain the odd numbers as 75, 77, 79, 81, 83, 85, 87, 89 and smallest odd number as 75
the average of four consecutive even numbers is 87
As seen earlier, 86 and 88 will be 2nd and 3rd even numbers.
i.e., 84, 86, 88 and 90 will be the even numbers and the second largest even number is 88
Therefore required sum is 75 + 88 = 163
⇒ Average of the 8 odd numbers = 656/8 = 82
the odd numbers immediately preceding and succeeding 82 are 81 are 83 respectively and these will be the middle numbers.
Therefore, we see that 4th and 5th odd numbers are 81 and 83 respectively.
Thus we can easily obtain the odd numbers as 75, 77, 79, 81, 83, 85, 87, 89 and smallest odd number as 75
the average of four consecutive even numbers is 87
As seen earlier, 86 and 88 will be 2nd and 3rd even numbers.
i.e., 84, 86, 88 and 90 will be the even numbers and the second largest even number is 88
Therefore required sum is 75 + 88 = 163
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The sum of eight consecutive odd numbers is 656. The average of four c...
Given information:
- The sum of eight consecutive odd numbers is 656.
- The average of four consecutive even numbers is 87.
To find:
- The sum of the smallest odd number and the second-largest even number.
Let's solve the problem step by step:
1. Finding the eight consecutive odd numbers:
- Let's assume the first odd number as 'x'.
- The next seven odd numbers will be 'x + 2', 'x + 4', 'x + 6', 'x + 8', 'x + 10', 'x + 12', and 'x + 14'.
- The sum of these eight odd numbers is 656, so we can write the equation as:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14) = 656
2. Finding the average of four consecutive even numbers:
- Let's assume the first even number as 'y'.
- The next three even numbers will be 'y + 2', 'y + 4', and 'y + 6'.
- The average of these four even numbers is 87, so we can write the equation as:
(y + (y + 2) + (y + 4) + (y + 6)) / 4 = 87
Now, let's solve these equations to find the values of 'x' and 'y':
1. Solving the equation for the sum of eight consecutive odd numbers:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14) = 656
8x + 56 = 656
8x = 600
x = 75
2. Solving the equation for the average of four consecutive even numbers:
(y + (y + 2) + (y + 4) + (y + 6)) / 4 = 87
4y + 12 = 348
4y = 336
y = 84
Now that we have found the values of 'x' and 'y', we can calculate the sum of the smallest odd number (x) and the second-largest even number (y + 4).
Sum = x + (y + 4) = 75 + (84 + 4) = 75 + 88 = 163.
Therefore, the sum of the smallest odd number and the second-largest even number is 163, which corresponds to option 'D'.
- The sum of eight consecutive odd numbers is 656.
- The average of four consecutive even numbers is 87.
To find:
- The sum of the smallest odd number and the second-largest even number.
Let's solve the problem step by step:
1. Finding the eight consecutive odd numbers:
- Let's assume the first odd number as 'x'.
- The next seven odd numbers will be 'x + 2', 'x + 4', 'x + 6', 'x + 8', 'x + 10', 'x + 12', and 'x + 14'.
- The sum of these eight odd numbers is 656, so we can write the equation as:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14) = 656
2. Finding the average of four consecutive even numbers:
- Let's assume the first even number as 'y'.
- The next three even numbers will be 'y + 2', 'y + 4', and 'y + 6'.
- The average of these four even numbers is 87, so we can write the equation as:
(y + (y + 2) + (y + 4) + (y + 6)) / 4 = 87
Now, let's solve these equations to find the values of 'x' and 'y':
1. Solving the equation for the sum of eight consecutive odd numbers:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14) = 656
8x + 56 = 656
8x = 600
x = 75
2. Solving the equation for the average of four consecutive even numbers:
(y + (y + 2) + (y + 4) + (y + 6)) / 4 = 87
4y + 12 = 348
4y = 336
y = 84
Now that we have found the values of 'x' and 'y', we can calculate the sum of the smallest odd number (x) and the second-largest even number (y + 4).
Sum = x + (y + 4) = 75 + (84 + 4) = 75 + 88 = 163.
Therefore, the sum of the smallest odd number and the second-largest even number is 163, which corresponds to option 'D'.
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The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?a)125b)144c)158d)163Correct answer is option 'D'. Can you explain this answer?
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