Based on an approximate solution of the Schrodinger equation, the effect that a pair of extremely short small-amplitude subcycle pulses has on a quantum system is studied. It is shown that, if the pulses are shorter than the inverse frequencies of atomic transitions, the probability of transitions between levels is determined by the electric area of the pulses and the time delay between them. As a consequence, a unipolar pulse can more efficiently affect the system than a bipolar one, while a sequence of pulses realizes a selective action on quantum objects, despite a nonresonant character of the interaction.