In 2003 Cordero-Erausquin, Fradelizi, and Maurey proved that the standard Gaussian measure satisfies a certain concavity property known as the (B) property. This (B) property has two versions, a weak version and a strong one. It is conjectured that any even log-concave measure satisfies at least the weak (B)-property. We will show that strong (B) property can fail even for arbitrarily small Gaussian perturbations on the standard Gaussian measure. We will also discuss some results and equivalent formulations of the above conjecture regarding the weak (B) property. Based on joint work with D.~Cordero-Erausquin.