Question

Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

Answer 1

The set with greater numbers is greater than the other set by 12 units.

Explanation:

Let us call
`A_1` the set with the smaller numbers and
`A_2` the other one. Each set has 4 consecutive positive integers and on integer in common. Then:

`A_1= \{a,a+1,a+2,a+3\}\\A_2=\{a+3,a+4,a+5,a+6\}`

The sum of all the numbers in A1 is:

`Sum_1=a+a+1+a+2+a+3=4a+6`

The sum of all number in A2 is:

`Sum_2=a+3+a+4+a+5+a+6=4a+18`

The differenc betwen the two sets is:

`R=4a+18-(4a+6)=4a+18-4a-6=18-6=12`

The set A2, the one with the grater numbers, is greater than the set A1 by 12 units.