Maths Olympiad Prep

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, 2026

Algebra Difficulty 1.3 Junior Find the answer Canada

Suppose that aa, bb, cc, dd
are four consecutive positive integers with a lt;b lt;c lt;d\text{a lt;b lt;c lt;d}. The value of (a+d)(b+c)(a+d)-(b+c) is

Pick one

Solution

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

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