Question

18) There are four consecutive odd integers. The sum of the three greatest is

27 more than the least. What is the least integer?

Please tell me the answer and how to solve it.​

Answer 1

This problem looks impossible: the sum of the three greatest odd numbers is an odd number.

On the other hand, the least odd number plus 27 (which is odd as well) is an even number.

So, if our four odd numbers are
`o_1,o_2,o_3,o_4`, you're asking that

`o_2+o_3+o_4=o_1+27`

The left hand side is odd, because it's a sum of three odd numbers

The right hand side is even, because it's the sum of two odd numbers.

An even number can't be equal to an odd number.