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There are 5 consecutive odd numbers. If the difference between the square of the average of first two odd numbers and the square of the average of last two odd numbers is 588, what is the smallest odd numbers?
- a)45
- b)47
- c)41
- d)49
- e)43
Correct answer is option 'A'. Can you explain this answer?
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There are 5 consecutive odd numbers. If the difference between the squ...
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There are 5 consecutive odd numbers. If the difference between the squ...
Approach:
To find the smallest odd number among 5 consecutive odd numbers, we need to first understand the given information and then solve for the answer. Let's break down the problem step by step.
Given:
- There are 5 consecutive odd numbers.
- The difference between the square of the average of the first two odd numbers and the square of the average of the last two odd numbers is 588.
Solution:
Let's assume the smallest odd number is x. Then the other consecutive odd numbers can be expressed as x+2, x+4, x+6, and x+8.
Now, according to the given information:
- Average of first two odd numbers = (x + x+2) / 2 = (2x + 2) / 2 = x + 1
- Average of last two odd numbers = (x+6 + x+8) / 2 = (2x + 14) / 2 = x + 7
The square of the average of the first two odd numbers = (x + 1)^2 = x^2 + 2x + 1
The square of the average of the last two odd numbers = (x + 7)^2 = x^2 + 14x + 49
Now, the difference between the two squares is given as 588:
(x^2 + 14x + 49) - (x^2 + 2x + 1) = 588
12x + 48 = 588
12x = 540
x = 45
Therefore, the smallest odd number is 45, which corresponds to option A.
To find the smallest odd number among 5 consecutive odd numbers, we need to first understand the given information and then solve for the answer. Let's break down the problem step by step.
Given:
- There are 5 consecutive odd numbers.
- The difference between the square of the average of the first two odd numbers and the square of the average of the last two odd numbers is 588.
Solution:
Let's assume the smallest odd number is x. Then the other consecutive odd numbers can be expressed as x+2, x+4, x+6, and x+8.
Now, according to the given information:
- Average of first two odd numbers = (x + x+2) / 2 = (2x + 2) / 2 = x + 1
- Average of last two odd numbers = (x+6 + x+8) / 2 = (2x + 14) / 2 = x + 7
The square of the average of the first two odd numbers = (x + 1)^2 = x^2 + 2x + 1
The square of the average of the last two odd numbers = (x + 7)^2 = x^2 + 14x + 49
Now, the difference between the two squares is given as 588:
(x^2 + 14x + 49) - (x^2 + 2x + 1) = 588
12x + 48 = 588
12x = 540
x = 45
Therefore, the smallest odd number is 45, which corresponds to option A.
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