2014 CEMC Gauss (Grade 7) Problems/Problem 8

Problem

If $9210 - 9124 = 210 - \boxed { }$ , the value represented by the $\boxed { }$ is

$\textbf{(A)}\ 296 \qquad\textbf{(B)}\ 210 \qquad\textbf{(C)}\ 186 \qquad\textbf{(D)}\ 124 \qquad\textbf{(E)}\ 24$

Let $x$ be the number represented by the box. We then have:

$9210 - 9124 = 210 - x$

$86 = 210 - x$

$x = 210 - 86$

$x = \boxed {\textbf {(D) } 124}$

We can notice that:

$9210 = 9000 + 210$

$9124 = 9000 + 124$

Thus, when subtracting the two, the $9000$ s cancel out, leaving $210 - 124$ .

This means that the number is $\boxed {\textbf {(D) } 124}$ , since we have the form $210 - \boxed { }$ .