2014 CEMC Gauss (Grade 8) Problems/Problem 3

Problem

The value of $(2014 - 2013) \times (2013 - 2012)$ is

$\textbf{(A)}\ 0 \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ 2 \qquad\textbf{(D)}\ 2014 \qquad\textbf{(E)}\ -1$

Solution 1

Using order of operations:

$(2014 - 2013) \times (2013 - 2012) = 1 \times 1 = \boxed {\textbf {(B) } 1}$

~anabel.disher

Solution 2

By the distributive property:

$(2014 - 2013) \times (2013 - 2012) = 2014 \times 2013 - 2013 \times 2013 - 2014 \times 2012 + 2013 \times 2012 = 2013 - 2012 = \boxed {\textbf {(B) } 1}$

~anabel.disher

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2014 CEMC Gauss (Grade 8) Problems/Problem 3

Problem

Solution 1

Solution 2