5. Karlson bought several pancakes (25 rubles each) and several jars of honey (340 rubles each) at the buffet. When he told Little Man how much he spent at the buffet, Little Man was able to determine, based on this information alone, how many jars of honey and how many pancakes Karlson bought. Could this amount have exceeded 2000 rubles?
Solution. Could. For example, let's say Karlson spent $4 \cdot 340 + 25 \cdot 40 = 2360$ rubles. Suppose Karlson can make up this amount in some other way; for this, he should spend x rubles less on pancakes and x rubles more on honey (or vice versa). But then, for x rubles, he can buy both a whole number of pancakes and a whole number of pots of honey. This means that x is divisible by both 25 and 340. But the smallest such x is 1700; however, Karlson cannot spend 1700 rubles less on either honey or pancakes.

## Criteria.

Example of a correct solution (7 points). "Yes, it is possible, for example, if Karlson bought 4 jars of honey and 40 pancakes. The number of pancakes can only be changed by 68, and the number of jars of honey - only by 5, but neither is possible." In general, we do not require strict formulations - it is enough to demonstrate an intuitive understanding of what is happening.

Errors. An example is given of what Karlson could buy, but it is not explained why this quantity fits - we give 5 points.

Progress. The author tries to give an example and justify it in the correct way, but the example itself turns out to be unsuitable (for example, due to an arithmetic error) - we give 2 points.

Zero points: only for the answer "could"; for any attempts to prove that it could not.