General aviation instructor reported a near miss with another aircraft on a training flight while in a practice area; in day; VMC conditions; while trying to communicate unsuccessfully with the other aircraft on a designated practice area CTAF frequency. The instructor maneuvered away from the other aircraft and landed safely.

Narrative

Aircraft X departed VGT and was given a frequency change to XXX.XX upon a right downwind departure to the northwest practice area. Upon switching to XXX.XX Aircraft X made an initial call giving their position and intentions. The CFI of Aircraft X also observed an aircraft in the practice area on ADSB at 6500 ft. around the water tower/west of the golf course. No response was heard from Aircraft Y. Aircraft X continued a climb out to 6500 and further to the West to avoid Aircraft Y. Throughout multiple calls and radio checks Aircraft Y did not respond. The instructor of Aircraft X verified the radio frequency multiple times and alerted traffic inbound to the practice area of Aircraft Y. At points Aircraft Y would start a track towards Aircraft X so Aircraft X would continue routine radio calls and go to other areas to the practice area.Eventually Aircraft X started maneuvering back towards VGT and started a descent. ADS-B showed Aircraft Y circling over the water tank at 4000 ft. Aircraft X descended over the water tank around 5500 ft. with traffic below now at 3800 ft. Over VPVKC at 4000 ft. Aircraft X made a last radio transmission to try calling Aircraft Y one last time and still received no response. Aircraft Y was on ADS-B at this point seemingly following Aircraft X 200 ft. below; to the left and behind; overtaking. Aircraft X started a right turn to gain distance from Aircraft Y. Aircraft X proceeded to switch to VGT Tower frequency; during that switch Aircraft Y started a climbing right turn that would cut off Aircraft X. (Observed by ADS-B by the CFI) Aircraft X cut power to idle and started a left turning descent at 30 degrees of bank. The occupants of Aircraft X observed Aircraft Y come into view from the bottom left of the windscreen and level off at the top right of the windscreen; reading 4000 ft. on ADS-B and infant of Aircraft X; Aircraft X was now at 3800 ft. We had essentially swapped positions.Aircraft X switched back to XXX.XX to try making contact with Aircraft Y and received no response. Aircraft X then switched back to VGT Tower and made an initial call to Tower stating they have traffic to their 1 o clock and above in sight. Several minutes later Aircraft Y calls into VGT Tower and is instructed to do a right 360 to follow Aircraft X in. Aircraft X made a call to Aircraft Y asking if they have radios in the practice area; and Aircraft Y responds that they do and were talking in the practice area. Aircraft X informed Aircraft Y that Aircraft X tried establishing communication throughout the flight and heard no response and informed Aircraft Y of the near miss. No other communications were observed from Aircraft Y regarding the incident. On the ground the CFI of Aircraft X informed another pilot of Aircraft Y's flight school of what had happened and that they would be contacting the flight school. Through the flight school and the CFI of Aircraft X learned that Aircraft Y was NOT on the right frequency for the practice area throughout the entire flight and that there was a DPE on board Aircraft Y performing a checkride that did not notice the issue. The northwest practice area does not require radio communications but it is an alert area and all aircraft are strongly advised to at least monitor XXX.XX due to the extensive training traffic. I strongly believe that without ADS-B a midair collision would've been drastically more likely than the outcome we received.