The correct statement out of the given options is 1 only.

Statement 1 states that if a country is experiencing an increase in its per capita GDP, its GDP must necessarily be growing. This statement is correct. Per capita GDP is the GDP divided by the population of a country. If the per capita GDP is increasing, it means that the GDP is growing at a faster rate than the population. Therefore, the overall GDP of the country must also be growing.

Statement 2 states that if a country is experiencing negative inflation, its GDP must be decreasing. This statement is not necessarily correct. Inflation and GDP are separate economic indicators. Inflation measures the rate at which prices of goods and services are increasing. GDP, on the other hand, measures the value of all goods and services produced in the country. While it is possible for negative inflation to coincide with a decrease in GDP, it is not always the case. Other factors such as changes in investment, government spending, and exports can also impact the GDP. Therefore, statement 2 is not necessarily true.

In conclusion, option 1, which states that only statement 1 is correct, is the correct answer.