Well... if I were asked this on the spot I'd first I'd first qualify I'm assuming a population mean of 0 (aka the distribution is centered). With this in mind, my reasoning would've been that the skewness would be the same as the normal, which is 0, because all symmetric distributions centered at 0 have 0 odd moments. The kurtosis would have to be greater than that of the normal because the tails of the t distribution are fatter BUT, as the degrees-of-freedom parameter increases, the kurtosis would become closer and closer to the normal, which is 3. (or an excess kurtosis of 0 if people prefer that).