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?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

Answer 1

Try this explanation, using algebra principles:
1) let the 1st set consists of integers: x; x+1; x+2; x+3, then, according to the condition, the 2d set consists of integers: x+3;x+4;x+5;x+6. Note, in this case 'x+3' is common integer.
2) The sum of 2d set is (x+3)+(x+4)+(x+5)+(x+6)=4x+18; the sum of the 1st set is x+(x+1)+(x+2)+(x+3)=4x+6.
The difference between the set with greater number and the another set is:
(4x+18)-(4x+6)=12.
PS. the same result is, when 'x' is common integer.

Answer 2

If you have two sets of integers {1, 2, 3, 4} and {4, 5, 6, 7}, then the sum of each set is 10 and 22, respectively, with a difference of 12. Based on logic, we know that this applies to any numbers you choose that meet the criteria. Number theory offers a more formalized outlook on these concepts.

The answer is D.