Question

Which of the following numbers is not the sum of three consecutive integers: 51, 61, 72, 81?

Answer 1

`61" "` it is the only one not divisible by 3.

Explanation:

One of the properties of any three consecutive numbers is that their sum is always a multiple of 3.

Why is this?

Consecutive numbers can be written as `x, x+1 , x+2, x+3 ,...`

The sum of 3 consecutive numbers is given by

`x + x+1 +x+2` which simplifies to

`3x + 3`

=`color(red)(3)(x+1)`

The `color(red)(3)` shows that the sum will always be a multiple of 3.

Which of the given numbers are divisible by 3?

You can simply add their digits to find out.
If the sum of the digits of a number is a multiple of 3, then the number itself is divisible by 3.

`51: 5+1 = 6" "` 51 is divisible by 3
`61: 6+1 = 7" "` 61 is not divisible by 3,
`72: 7+2 =9" "` 72 is divisible by 3
`81: 8+1 = 9 " "`81 is divisible by 3

Only 61 is not divisible by 3. Therefore it is not the sum of three consecutive numbers.