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Problem 107

Algebra Difficulty 1.3 Multiple choice CEMC Fermat · Canada · 2026

Suppose that $a$ , $b$ , $c$ , $d$
are four consecutive positive integers with $a<b<c<d$ . The value of $(a+d)-(b+c)$ is

Pick one

Official solution

Since $a$ , $b$ , $c$ , $d$
are four consecutive positive integers, then $b=a+1$ , $c=a+2$ , and $d=a+3$ . Thus the value of $(a+d)-(b+c)=(a+a+3)-(a+1+a+2)=(2a+3)-(2a+3)=0$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.