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Mathland Election

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.

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One or Both

Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

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Matching Fractions Decimals Percentages

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

Weekly Problem 3 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Let $c$ denote the size of the class and $g$ denote the number of girls. We want $0.45c< g< 0.5c\Leftrightarrow 0.45< \frac{g}{c}< 0.5$.

If we try $g=1$ there is no such $c$, since if $c=1$ or $c=2$, $\frac{g}{c}$ is too large, and if $c> 2$, $\frac{g}{c}$ is too small.

Similarly for $g=2$, $3$ or $4$. However for $g=5$ setting $c=11$ leads to $\frac{g}{c}=\frac{5}{11}=\frac{500}{11}$% $=(\frac{440}{11}+\frac{60}{11})$% $=(40+\frac{55}{11}+\frac{5}{11})$% $=45\frac{5}{11}$%.

This problem is taken from the UKMT Mathematical Challenges.

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