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Problem 81

Algebra Difficulty 1.2 Find the answer CEMC Pascal · Canada · 2020

The value of $\dfrac{2^4-2}{2^3-1}$ is

$1$
$0$
$\frac{7}{4}$
$\frac{4}{3}$
$2$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

We note that $2^3 = 2 \times 2 \times 2 = 8$ and $2^4 = 2^3 \times 2 = 16$ .

Therefore, $\dfrac{2^4-2}{2^3-1} = \dfrac{16-2}{8-1} = \dfrac{14}{7} = 2$ .

Alternatively, $\dfrac{2^4 - 2}{2^3-1} = \dfrac{2(2^3-1)}{2^3 - 1} = 2$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.