Maximum neutron-star mass as a function of two parameters of quark matter when the density at which the transition from nucleonic to quark matter occurs is equal to 1.5 times the nuclear saturation density. The measurement of a pulsar mass of ⩾1.93  M _☉ from Shapiro delay observations indicates that, if the transition to quark matter occurs at densities that are relevant to neutron star interiors, such a massive star can be supported against collapse only if the quarks are strongly interacting ( a ₄ ⩽ 0.63).