Question

Find the two consecutive odd numbers whose sum is 76.
$
  (a){\text{ 77 and 39}} \\
  (b){\text{ 37 and 39}} \\
  (c){\text{ 37 and 99}} \\
  (d){\text{ 56 and 39}} \\
$

Answer 1

Hint: In this question let the first odd number be any variable say x, so the next consecutive odd number will be (x +2). Then use the constraints of the questions to formulate an equation that will help finding the value of this variable.

Complete-step-by-step solution -
Let the first odd number be x.
Now if we add 1 in any odd number so the number becomes even for example (3 + 1 = 4) so 4 is an even number. Therefore, we have to add 2 to make a consecutive odd number so the second consecutive odd number is (x + 2).
So according to question we have,
$x + \left( {x + 2} \right) = 76$
Now simplify the above equation we have,
$ \Rightarrow 2x = 76 - 2 = 74$
$ \Rightarrow x = \dfrac{{74}}{2} = 37$
So the second consecutive odd number = (x + 2) = (37 + 2) =39
So the two consecutive odd numbers are 37 and 39.
So this is the required answer.
Hence option (B) is correct.

Note: Odd numbers come under the sub category of whole numbers such that they cannot be exactly divided into equal pairs. Another definition of odd numbers is that these numbers are not exactly divisible by 2, that means the remainder of these numbers when divided by 2 is not 0, however it is somewhat like 1,3,5,7,9…….. and the interesting point is these are also the subsequent odd numbers.