Maths Olympiad Prep

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, 2014

Algebra Difficulty 1.2 Junior Find the answer Canada

If 2n+5=162n+5 = 16, the expression 2n32n-3 equals

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Solution

Since 2n+5=162n+5=16, then 2n3=(2n+5)8=168=82n-3 = (2n+5)-8 = 16-8=8.

Alternatively, we could solve the equation 2n+5=162n+5=16 to obtain 2n=112n=11 or n=112n = \frac{11}{2}.

From this, we see that 2n3=2(112)3=113=82n-3 = 2(\frac{11}{2})-3=11-3=8.

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