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We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthrough first argument, but simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their `quality'. We also consider the metric quantitative theory of Diophantine approximations, improving the ( (N) ) ^-C error-term of Aistleitner-Borda and the first named author to (- ( (N) ) ^1{2 - }).
Hauke et al. (Tue,) studied this question.
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