The correct answer is that the most gas exchange occurs at the bottom of the lung as some in this thread has correctly pointed out. I don't know what the author of that book has been smoking.
The apex of the lung is the least ventilated part of the lung due to the fact that the compliance of the lung is not constant but instead decreases as the pressure gradient over the alveolar wall increases. Due to the weight of the lung, the interstitial pressure is higher in the base of the lung. As the air pressure in the alveoli is constant, this means that the pressure gradient is lower at the base and hence this part of the lung is better ventilated.
The high V/Q at the apex is the equivalent of a physiological dead space which obviously impairs the gas exchange in this part of the lung as part of the small amount of ventilation that goes to this part of the lung is wasted. However I fail to see how the low V/Q at the base of the lung impairs the efficiency in the utilization of the ventilated air. Rather the lack of ventilation makes the perfusion inefficient resulting in a physiologic shunt. Hence the low V/Q at the base, even if it impairs the efficiency of the lung as a whole due to wasted perfusion, actually shows that the air that is ventilated is used more efficiently at the base than in the other parts of the lung. This is illustrated by the fact that the PCO2 and PO2 here is closer to the values in the venous blood.*
As the base of the lung, which is the best ventilated part of the lung, also extracts more oxygen out of each unit of ventilated air, we can conclude that most of the gas exchange occurs at the base and not the apex of the lung. It is not, however, due to a V/Q that is closer to 1, as it is in fact less than 1 at the bottom of the lung.
*As the PO2 in the inspired air is constant, a lower PO2 in the alveoli shows that more of the oxygen in the exchanged air has been absorbed by the blood, as the amount of oxygen in the air is proportional to the partial pressure of oxygen.