In 1980, Country A had a per capita gross domestic product (GDP) that was $5,000 higher than that of the European Economic Community.
Conclusion
The average standard of living must have risen in A from 1980 to 1990.
Evidence (Since)
Rising GDP indicates a rising average standard of living.
and, Country A went from being $5k higher than Europe in 1980 to $6k higher than Europe in 1990.
Evaluate
For the author to prove average standard of living went up, he needs to establish that from 1980 to 1990, per capita GDP in country A was rising.
But all he established was that country A's GDP advantage over European countries widened from 1980 to 1990.
If you went from making 10 grand more than your best friend to making 15 grand more than your best friend, does that mean you are making 5 grand more or your best friend is making 5 grand less (or any combination of both of you changing that has that net result).
This is the classic Relative vs. Absolute, or % vs. # distinction that LSAT likes to test.
The author assumes that because Country A's GDP is rising in relation to the European countries, that it is rising in absolute terms.
Goal
The author fundamentally is assuming that Country A's per capita GDP is rising. She's assuming that one indication of that is the widening advantage Country A has over Europe, when it comes to GDP.
Since it would weaken the argument if we were to say, , the argument has to assume that Europe does not have declining GDP.