13. Four brothers have different heights. Tobias is shorter than Victor by the same amount by which he is taller than Peter. Oscar is shorter than Peter by the same amount as well. Tobias is $184 \mathrm{~cm}$ tall and the average height of all the four brothers is $178 \mathrm{~cm}$. How tall is Oscar?
A $160 \mathrm{~cm}$
B $166 \mathrm{~cm}$
C $172 \mathrm{~cm}$
D $184 \mathrm{~cm}$
E $190 \mathrm{~cm}$
13. A Let $k \mathrm{~cm}$ be the difference between the heights.
Then the heights in $\mathrm{cm}$ are: Tobias 184, Victor $184+k$, Peter $184-k$, and Oscar $184-2 k$. The mean is 178 so $\frac{1}{4}(184+184+k+184-k+184-2 k)=178$. Hence $4 \times 184-2 k=4 \times 178$, giving $2 k=4 \times 184-4 \times 178=4 \times 6=24$. Hence $k=12$. Therefore Oscar's height in $\mathrm{cm}$ is $184-2 \times 12=160 \mathrm{~cm}$.