Maths Olympiad Prep

Library / /219 of 434

, 2019

Combinatorics Difficulty 1.2 Junior Find the answer Canada

Based on the graph shown, how many vehicles had an average speed of at least 80 km/h?

Figure 0

Pick one

Solution

When x=3x=3, 2xamp;=2×3=63x1amp;=3×31=8x+5amp;=3+5=87xamp;=73=46+2xamp;=6+2×3=12\begin{align*} 2x&=2\times3=6\\ 3x-1&=3\times3-1=8\\ x+5&=3+5=8\\ 7-x&=7-3=4\\ 6+2x&=6+2\times3=12 \end{align*} Of the given answers, 3x1=83x-1=8 is the only one of the given equations which is true when x=3x=3.

Figure for this problem

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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