User:Arotenbe/Solutions to IQ sample test

Jump to: navigation, search

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 ${\displaystyle {\frac {1}{0}}}$.

2. We solve the equation ${\displaystyle A={\frac {1}{2}}bh}$ for ${\displaystyle h}$, giving us ${\displaystyle h={\frac {2A}{b}}}$. To calculate the area of the triangle, we use Heron's formula, ${\displaystyle A={\sqrt {s\left(s-a\right)\left(s-b\right)\left(s-c\right)}}}$ where ${\displaystyle s={\frac {a+b+c}{2}}}$. Plugging the value of ${\displaystyle s=25}$, we see that ${\displaystyle A={\sqrt {25\left(25-9\right)\left(25-16\right)\left(25-25\right)}}}$, 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 ${\displaystyle 2=1}$. From this, we have that ${\displaystyle 2+2=2}$. However, ${\displaystyle 2\neq 1}$, so by vacuous truth, ${\displaystyle 2+2=5}$ for all non-zero values of 2. Q.E.D.