We studied the $^{12}$C(p,2p+n) reaction at beam momenta of 5.9, 8.0 and 9.0 GeV/c. For quasielastic (p,2p) events we reconstructed {bf p_f} the momentum of the knocked-out proton before the reaction; {bf p_f} was then compared (event-by-event) with {bf p_n}, the measured, coincident neutron momentum. For $|p_n|$ > k$_F$ = 0.220 GeV/c (the Fermi momentum) a strong back-to-back directional correlation between {bf p_f} and {bf p_n} was observed, indicative of short-range n-p correlations. From {bf p_n} and {bf p_f} we constructed the distributions of c.m. and relative motion in the longitudinal direction for correlated pairs. After correcting for detection efficiency, flux attenuation and solid angle, we determined that 49 $pm$ 13 % of events with $|p_f|$ > k_F had directionally correlated neutrons with $|p_n|$ > k$_F$. Thus short-range 2N correlations are a major source of high-momentum nucleons in nuclei.