# User:Arotenbe/Solutions to IQ sample test

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I here reveal my solutions to the IQ sample test.

More coming soon...

## editSolutions

0. We are not allowed to use any symbols in the set (n, x, ∞). However, we can still use other symbols, so we define infinity as $\frac{1}{0}$.

2. We solve the equation $A = \frac{1}{2} bh$ for $h$, giving us $h = \frac{2A}{b}$. To calculate the area of the triangle, we use Heron's formula, $A = \sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ where $s = \frac{a+b+c}{2}$. Plugging the value of $s = 25$, we see that $A = \sqrt{25 \left(25-9\right)\left(25-16\right)\left(25-25\right)}$, which is 0. Hence, the triangle has a height of 0 dollars. Or infinity dollars. Whatever.

4a. From the given, we know that the angle is 90 degrees, so the error is 0%.

4b. We use a proof by induction. We start with the base case of $2 = 1$. From this, we have that $2 + 2 = 2$. However, $2 \neq 1$, so by vacuous truth, $2 + 2 = 5$ for all non-zero values of 2. Q.E.D.