Republican presidential candidate Carly Fiorina is having it two ways — or even three — when it comes to gender politics.

As a candidate in a party that tends to abhor interest-group politics, the former Hewlett-Packard CEO sometimes explicitly rejects her gender as an issue in the race. At other times, though, she uses her additional X chromosome as a shield — and sometimes wields it as a sword.

Both tendencies have been on display during a surge that has vaulted her from obscurity to contention.

Take the second Republican presidential debate last week at the Ronald Reagan Presidential Library. The only woman on the stage, she was also the only candidate who refused to pander when CNN’s Jake Tapper asked which woman should replace Alexander Hamilton on the $10 bill. The male candidates gave answers that ranged from their wives or mothers to foreign politicians to historical figures.

Fiorina rejected the premise of the question: “I wouldn’t change the $10 bill, or the $20 bill. I think, honestly, it’s a gesture. I don’t think it helps to change our history. What I would think is that we ought to recognize that women are not a special interest group.”

Yet, Fiorina’s signature moment in that debate was a dress-down of Donald Trump for his putdown of her face. The real estate mogul later insisted he was talking about her persona.

Fiorina’s now-famous response at the debate was a bid for gender solidarity: “I think women all over this country heard very clearly what Mr. Trump said.”

Fiorina’s now-famous response at the debate was a bid for gender solidarity: “I think women all over this country heard very clearly what Mr. Trump said.”

In an interview with CNBC just before to the debate, Fiorina said women, alone, must deal with questions about their appearance on the campaign trail.

“A man would not be asked on national television whether his hormones prevented him from serving in the Oval Office,” she said. “Donald Trump has said many things about other candidates. But he has not talked about their appearance.”

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Christian Grose, a political science professor at the University of Southern California, said the issue is not absent from her strategy.

“There’s definitely a gender component to her campaign,”  he said.

But Grose said much of the time Fiorina has spent talking about her gender has been in response to questions, not issues she raised independently. That was the case with the putdown of Trump during the debate.

“I thought she handled that really well,” he said. “That was a question that came to her … She was very concise in a way that it was about her, not to empower gender.”

Despite the implication, female candidates are not alone in having to deal with questions or ridicule based on looks. Trump has both been a target of ridicule based on appearance — look at his hair — and has dished insults to male opponents. At the debate, he joked that he had “plenty of subject matter” to go after Sen. Rand Paul based on physical appearance.

Fiorina herself once succumbed to the temptation to ridicule an opponent based on looks. An open mic during her failed race for the U.S. Senate in California recorded her mocking opponent Barbara Boxer’s hairstyle. “God, what is that hair? So yesterday!” she told staff while the camera rolled at a local TV station.

During an appearance on “The Laura Ingraham Show” earlier this month, Fiorina said it was “sexist” to suggest that her real goal in the 2016 campaign was a spot as the vice presidential running mate.

“No one talks about the men being in it to be veep. I’m not in it to be veep. I’m in this to win this job and to do this job,” she said.

It wasn’t the first time she made the charge. During an interview with Yahoo Global News anchor Katie Couric shortly after announcing her candidacy in May, Fiorina lashed out when the anchor raised the veep question. “Oh Katie, would you ask a male candidate that question?” she said.

Fiorina’s sexism allegation, however, is odd in light of the fact that many low-polling male candidates have had to contend with the question over the years. John Edwards denied it throughout the 2004 primary season before accepting John Kerry’s invitation to be his running mate. Former New Mexico Gov. Bill Richardson dealt with it in 2009.

In the current campaign, in fact, panelists on “The Last Word with Lawrence O’Donnell” on MSNBC in April speculated that Marco Rubio’s real aim might be the vice presidency. And during an appearance on CNN’s “State of the Union” in August, Ben Carson fielded a question about whether he would be Donald Trump’s running mate. (For the record, he said anything was possible).

“It’s not only not new, it’s something that comes up” almost every election, said Joel Aberbach, a political science professor at the University of California, Los Angeles. “For the most part, they deny it.”

Grose said he thinks Fiorina has a point on veep speculation.

“I don’t think anyone has asked Donald Trump if he’s really running for vice president, and they have the same political experience,” he said.

Some of the rationale of Fiorina’s campaign is based on gender — both a rejection of it as part of identity politics of the left and appeal to it on grounds that it gives her a unique advantage.

Some of the rationale of Fiorina’s campaign is based on gender — both a rejection of it as part of identity politics of the left and appeal to it on grounds that it gives her a unique advantage in a race against a Democratic nominee that is likely to be female.

On “The Kelly File” on Fox News Channel in April, she suggested that her sex should have not bearing on the race.

“It’s not about your gender, it’s about what you believe, what your accomplishments are, what your track record is, what your leadership is,” she said.

That same month, Fiorina told reporters at a Christian Science Monitor breakfast: “I think that if Hillary Clinton were to face a female nominee, there are a whole set of things that she won’t be able to talk about. She won’t be able to talk about being the first woman president. She won’t be able to talk about a war on women without being challenged. She won’t be able to play the gender card.”

Aberbach said he thinks Fiorina has done a good job in the debates and is smart to distinguish herself from her GOP competitors as someone who could go toe-to-toe with Clinton without looking sexist.

“She’s pretty well-positioned,” he said. “The odds are the Democrats are going to nominate a woman.”

Grose said Fiorina’s tactical advantage was evident in her answer to the $10 bill question.

“She was able to answer it differently than a male candidate could,” he said.