1. Kolya says that two chocolate bars are more expensive than five gums, Sasha - that three chocolate bars are more expensive than eight gums. When this was checked, only one of them was right. Is it true that 7 chocolate bars are more expensive than 19 gums? Don't forget to justify your answer.
Solution. Let the price of a chocolate bar be $c$, and the price of a piece of gum be $g$. Kolya says that $2 c>5 g$ or $6 c>15 g$, while Sasha says that $3 c>8 g$ or $6 c>16 g$. If Sasha were correct, Kolya would also be correct, which contradicts the condition. Therefore, Kolya is right, but not Sasha, and in fact $3 c \leqslant 8 g$ or $21 c \leqslant 56 g<57 g$, which means $21 c<57 g$ and $7 c<19 g$. Answer: false.

Criteria. Only the answer - 0 points. Only specific cases of concrete prices for chocolate bars and pieces of gum - no more than 1 point. Additional conditions are introduced into the problem, such as assumptions about monetary units - no more than 1 point. The proof is entirely based on relations of the type " $\approx$ (approximately equal) - no more than 1 point.