"We have a lot of smart people. We have by far the highest IQ of any Cabinet ever selected," Trump said at a luncheon in his honour at the Trump International Hotel in Washington DC.
Addressing the luncheon, he gave a shout-out to his Cabinet picks, including his choice for Attorney General Jeff Sessions, Tom Price, Trump's nominee to lead Health and Human Services and Indian-American Nikki Haley, his US envoy to the United Nations.
In his remarks, Trump mentioned he had sent Haley "over to speak to China" without saying anything further.
He also said his pick for Treasury Secretary Steven Mnuchin is "right now getting grilled" during his confirmation hearing at the Senate and "he is doing a great job, fantastic job".
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Before addressing the gathering, Trump invited his wife and incoming First Lady Melania to speak.
Trump was also joined by his family at the event. The incoming President arrived in Washington earlier in the afternoon and has a day full with inaugural engagements, including a concert in the evening at the Lincoln Memorial.
He will also be visiting the Arlington Cemetery for a wreath laying ceremony and will have a candle light dinner in the evening.