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

1 Answer
Oct 19, 2016

Answer:

#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.