Is it possible to have a Mach number greater than 1 at the throat?

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I have a problem for my Gas Dynamics homework, in which the problem asks to solve for the Mach number at the throat of a converging-diverging nozzle.

I assumed that the Mach at the throat should be equal to 1 since the professor said it was impossible to have a Mach number greater then 1 at the throat.

After showing the same problem to a Graduate Student I work with he showed me that it is possible to have a Mach number greater then 1 at the throat through the area ratios.

But after speaking to my professor a second time he has again said it is not possible.

So my question is.. is it possible to have a Mach number greater than 1 at the throat.


Oh the conditions for the problem are as follows:
Mi=2
Ai=20 cm^2

Athroat=15cm^2

Shock Area=22 cm^2
Ae=25cm^2

where gamma= 1.4

according to the solutions Mach at the throat equals 1.662


I assumed it was 1 but it was not correct.


If someone could steer me in the right direction I'd appreciate it thanks!