Step 1: Anchor HCG to trophoblastic tissue.
HCG in germ cell tumors always comes from syncytiotrophoblast-type cells, the same cells that make HCG during a real pregnancy. So the question is really asking which of these four tumors has no trophoblastic component.
Step 2: Go through the trophoblast-containing ones.
Choriocarcinoma is built entirely from trophoblast, so HCG is always sky high. Polyembryoma contains embryoid bodies with a trophoblastic rim, so it also makes HCG. Embryonal carcinoma is undifferentiated but frequently has scattered giant cells of trophoblastic type mixed in, which is why it can secrete AFP, HCG, or both.
Step 3: Look at the yolk sac tumor separately.
The endodermal sinus tumor copies the fetal yolk sac, a structure that makes AFP in a developing fetus, not HCG. Since it has no trophoblastic differentiation, HCG stays normal while AFP rises.
Step 4: Pick the odd one out.
Three of the four tumors carry trophoblastic tissue and raise HCG. The endodermal sinus tumor does not.
\[ \boxed{\text{Endodermal Sinus Tumor}} \]