Increase in per capita GDP always means GDP is growing?
Your reasoning seems correct.

if we consider that Gp=G/(population) and we know that Gp is increasing then we have the following possibilities:


if (population) is static or growing then we can conclude that G must necessarily be growing
if (population) is decreasing then G can be either static or actually decreasing slower than (population). In this case, the statement on the question fails