President Trump and Secretary of State Rex Tillerson listen to world leaders before a luncheon in New York City on Sept. 21. (AFP/Getty Images)

Who would win in an IQ faceoff, President Trump or Secretary of State Rex Tillerson?

Of all the pressing questions Americans have for their government right now, that one is pretty far from the top of the list.

But the world’s foremost group of verified smart people has offered to help answer it anyway.

Mensa, the international high-IQ society, said it would be willing to administer its qualifying test to the two men after a feud over their respective brainpower appeared to boil over on Tuesday.

The spat almost reads like something out of the Onion, so bizarre that it could pass as satire.

It started last week when NBC News, The Washington Post and other outlets reported that Tillerson had called the president a “moron” and questioned his understanding of foreign policy. Trump responded by challenging his top diplomat to a mental duel.

“I think it’s fake news,” he told Forbes magazine in an interview published Tuesday, “but if he did that, I guess we’ll have to compare IQ tests. And I can tell you who is going to win.”

President Trump and his Secretary of State Rex Tillerson have been on shaky ground for weeks, and Trump's challenge of an 'IQ test' face-off with Tillerson isn't smoothing things over. Here's a look back at where their relationship derailed. (Jenny Starrs/The Washington Post)

White House press secretary Sarah Huckabee Sanders later called the comment “a joke and nothing more than that.”

But that didn’t stop Mensa from jumping into the fray.

“American Mensa would be happy to hold a testing session for President Trump and Secretary Tillerson,” Charles Brown, the organization’s communications director, told the Hill on Tuesday.

Mensa calls itself the largest organization of people with very high IQs, claiming more than 50,000 members in the United States and more than 130,000 worldwide. To qualify as a member, applicants must score in the 98th percentile or above on an IQ test. There are more than 200 such tests that Mensa accepts, but the organization only administers one itself, known simply as the Mensa Admissions Test.

The Trump-Tillerson dust-up came at an opportune time for the organization, which tends to schedule more tests in October than any other month. Mensa mentioned as much in a news release Tuesday, saying people from all walks of life could partake, “even politicians.”

“Their beliefs and jobs are trumped by their IQ scores,” the release read. “At Mensa, all brilliance is welcome.”

In an interview later in the day with CBS, Brown, the spokesman, asked people not to take its proposal too seriously.

“When we were asked earlier about President Trump’s IQ and IQ testing . . . we just thought it would be fun to invite the president and Secretary Tillerson to take our test — not as a challenge or any kind of political commentary — really it’s just more about highlighting a special month for us,” Brown said. “October of 1946 was when our organization was founded and every October we take advantage of that to encourage admissions tests.”

Of course, many experts argue that IQ testing is fundamentally flawed and doesn’t measure a person’s true intelligence. As Tom McKay at Gizmodo notes, IQ tests are biased toward qualities that reflect social standing — things like academic achievements — rather than the innate abilities of a person’s brain.

On Tuesday night, “The Late Show With Stephen Colbert” poked fun at the spat in a tweet: “EXCLUSIVE: We have the results of the Rex Tillerson and Donald Trump IQ Test challenge.” The tweet featured an image of bogus test scores.

Let’s just say things didn’t look so hot for the president.