2006 CEMC Fermat Problems/Problem 3

Problem

The value $\frac{4^3}{10^2 - 6^2}$ is

$\text{ (A) }\ 1 \qquad\text{ (B) }\ 0.5 \qquad\text{ (C) }\ -35.36 \qquad\text{ (D) }\ 1.5 \qquad\text{ (E) }\ 4$

Solution 1

We can just simplify the fraction:

$\frac{4^3}{10^2 - 6^2} = \frac{64}{100 - 36} = \frac{64}{64} = \boxed {\textbf {(A) } 1}$

~anabel.disher

Solution 1.5

We can also use difference of squares to find the value of the denominator: $\frac{4^3}{10^2 - 6^2} = \frac{64}{(10 - 6)(10 + 6)} = \frac{4 \times 16}{4 \times 16} = \boxed {\textbf {(A) } 1}$

~anabel.disher

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2006 CEMC Fermat Problems/Problem 3

Problem

Solution 1

Solution 1.5