M20P PLT AND A LIGHT TWIN HAD AN NMAC IN NCT CLASS E.

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ATC DSNDED US TO 2000 FT MSL WITH ASSIGNED HDG. COLLISION AVOIDANCE ALARM SOUNDED. PAX WARNED OF NEARBY ACFT. I GOT VISUAL ON THE ACFT AS WE WERE ON COLLISION COURSE. I BANKED 50 DEGS TO L AND DOVE DOWN. I MENTIONED TO ATC THAT COLLISION WAS AVOIDED; AND THAT I BELIEVED WE WERE NOW IN FRONT OF THE OTHER ACFT. I ASKED HIM IF THE TWIN WAS GAINING ON US. HE PAUSED AND SAID SOMETHING TO THE EFFECT THAT HE CALLED TFC; AND I WAS AT THE WRONG ALT. I MENTIONED TO HIM I DOVE DOWN TO AVOID THE OTHER ACFT. HE THEN TOLD ME TO STAY AT 2000 FT; AND NOTIFY HIM OF ARPT IN SIGHT. I CALLED ARPT IN SIGHT. HE SAID 'CLRED FOR THE VISUAL APCH; MAKE R DOWNWIND FOR RWY 30. I DSNDED FOR THE DOWNWIND. AT 1500 FT HE ASKED ALT; AND SAID HE TOLD ME TO 'MAINTAIN 2000 FT' UNTIL ESTABLISHED ON THE DOWNWIND.' ATC VERY BUSY AT THE TIME. I CLBED TO 2000 FT AND WAS TURNED OVER TO TWR. CONTRIBUTING FACTOR WAS THAT ATC WAS OVER WORKED AND CTLING TOO MANY AIRPLANES. HE WAS TALKING VERY FAST AND OFTEN TIMES HARD TO UNDERSTAND. PLT NEEDS TO BE CLR ON ALL CLRNCS. WHAT I HEARD; AND WHAT HE SAID; WERE 2 DIFFERENT THINGS.