# User:Arotenbe/Solutions to IQ sample test

I here reveal my solutions to the IQ sample test.

More coming soon...

## Solutions

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.