In a certain game, different colors of gems are worth different amounts of gold pieces (GP). Red gems are worth 3 GP each, and blue gems are worth 7 GP each. Assuming that you can obtain an unlimited amount of only red and/or blue gem, what is the largest GP value of gems that you can have?

The critical statement for solving this problem is

"Assuming that you can obtain an unlimited amount of only red and/or blue gems"

If we can obtain an unlimited amount, there is virtually no limit imposed on the value of gold pieces we can have.

Thus,

There is no finite largest value we can have.