2008 Grade 8 CEMC Gauss Problems/Problem 1

Problem

The value of $8 \times (6 - 4) + 2$ is

$\text{ (A) }\ 46 \qquad\text{ (B) }\ 20 \qquad\text{ (C) }\ 18 \qquad\text{ (D) }\ 12 \qquad\text{ (E) }\ 56$

Solution 1

We can use order of operations to evaluate the expression:

$8 \times (6 - 4) + 2 = 8 \times 2 + 2 = \boxed {\textbf {(C) } 18}$

~anabel.disher

Solution 2

We can subtract $2$ from each answer choice, and see if the result is divisible by $8$ (which works because $2$ plus a multiple of $8$ is what we are looking for in the problem:

$46 - 2 = 44$ , which is not a multiple of $8$

$20 - 2 = 18$ , which is not a multiple of $8$

$18 - 2 = 16$ , which is a multiple of $8$

$12 - 2 = 10$ , which is not a multiple of $8$

$56 - 2 = 54$ , which is not a multiple of $8$

The only answer choice that is $2$ more than a multiple of $8$ is $\boxed {\textbf {(C) } 18}$

~anabel.disher

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2008 Grade 8 CEMC Gauss Problems/Problem 1

Problem

Solution 1

Solution 2