The sum of three consecutive odd numbers is 57. Find the numbers.

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17, 19 and 21

19, 15 and 25

13, 17 and 26

21, 13 and 29

answer is A.

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Detailed Solution

Concept- Here, we will initially attempt to use a single variable, n, to represent the three successive odd numbers. Then, in order to determine the value of n as well as the values of three successive odd integers, we shall equate their sum to 57.
Since we are aware that every odd number has the form (2k + 1) , Because we are aware that an odd number cannot be divided by 2, we express odd numbers in this way.
The following odd number will be (2k+3) since (2k+2) is plainly divisible by 2, as can be shown if we take it.
The difference between any two successive odd numbers is therefore:
Question Image

Therefore, there is a difference of 2 between every pair of consecutive odd numbers.
Let's assume that 'n' is an odd number right now.
the odd number that comes before n will therefore be (n-2) .
Additionally, there will be an odd number (n+2) right after n.
The fact that these three successive odd numbers add up to 57 is known. Thus, we can formulate the equation shown below:
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Before n, the odd number will be = n -2 = 19 -2 = 17.
The following odd number will be = n+2 = 19 + 2 = 21
Therefore, 17, 19, and 21 are the needed three consecutive odd numbers.
Hence, the correct answer is option 1.

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