Donald Trump talks a big game, but how much of it is true?

Republican presidential candidate Donald Trump can be a divisive figure, but everyone seems to agree that the billionaire businessman speaks his mind. Whether he always speaks the truth is another question.

"One of the things I respect about Donald Trump is he's willing to stand up and speak the truth and willing to take on Washington," Sen. Ted Cruz of Texas, Trump's 2016 GOP rival, said Wednesday after meeting with Trump in New York.

Ironically, Trump hasn't always been straight about his take on Cruz's candidacy. When asked about whether Cruz should be eligible for the presidency even though he was born in Canada, Trump told Politico this week, "I don't know. I mean I haven't looked at it. I have not looked at it at all." Yet as Politico pointed out, Trump said in March that Cruz's birthplace is "a hurdle."

Click through for a look at some of Trump's bold remarks from the past week.

Trump's net worth: $1 billion more than in June?

When Trump announced his candidacy in mid-June, he estimated that his net worth was just under $9 billion.

This week, Trump said his net worth is about $1 billion more than that, thanks to rising real estate values in New York, San Francisco, Miami and other cities where he has property.

CBS News has requested Trump's FEC financial disclosure to see whether there is any more detail that would shed light on this claim, but the FEC has not yet supplied it.

Without more information, it's hard to know whether Trump's real estate holdings increased in value that much in the past month. However, the latest data from online real estate company Zillow shows that residential real estate markets have been on an upward trend in the cities where Trump has property:

In New York City, for instance, home values grew 5.2 percent from May 2014 to May 2015, and 0.4 percent from April 2015 to May 2015. In San Francisco, home values grew 12.4 percent from May 2014 to May 2015, and 1.9 percent from April 2015 to May 2015. In Miami, home values grew 5.1 percent from May 2014 to May 2015, and 0.5 percent from April 2015 to May 2015.

Trump slams Jeb Bush for sanctuary cities

Donald Trump has repeatedly slammed his GOP competitor former Florida Gov. Jeb Bush as weak on immigration.

"How can I be tied with Jeb Bush?" Trump said at a rally Saturday at the Phoenix, Arizona convention center. "He's terrible. He's weak on immigration. Sanctuary cities. Did you know that he had five of them in Florida when he was governor?"

Bush was governor of Florida from 1997 until January 2007. It's hard to say definitively whether there were any so-called sanctuary cities, which deliberately avoid enforcing federal immigration laws, in Florida during Bush's tenure as governor. Some "sanctuary" policies are official policy, while others are more informal.

San Francisco under fire for "sanctuary" immigration policy

However, public records suggest that Bush didn't govern over any official sanctuary cities; in fact, his state seemed uniquely ready to help the federal government enforce immigration laws. While Bush was governor, his brother George W. Bush was president.

In 2006, when Congress was considering an immigration overhaul, the nonpartisan Congressional Research Service produced a list of 31 cities and counties that "will generally promote policies that ensure such aliens will not be turned over to federal authorities." None of those cities or counties were in Florida.

Meanwhile, on July 29, 2005, members of Congress held a hearing to discuss issues like Section 287(g) of the Immigration and Nationality Act. That part of the law enabled local police departments to work with federal immigration officers to identify illegal immigrants.

"Only two states in the Union and one county participate in 287(g) Program. Florida is one of them," then-Rep. Kendrick Meek, D-Florida, pointed out in the hearing.

Rep. Mike Rogers, R-Alabama, who presided over the hearing, noted that Florida at that point had already authorized the training of 35 state and local law enforcement officers for the program. In addition to that, the Florida Regional Domestic Security Task Forces performed immigration enforcement functions as a part of their investigations.

News articles suggest that Miami-Dade County has for the past decade been considered an unofficial sanctuary county by some, though Bush has said that he opposes them.

Trump: "I'm going to win the Hispanic vote"

At a Thursday night event in New Hampshire, Donald Trump repeated his assertion that Hispanic voters "love" him and will vote for him, in spite of his inflammatory rhetoric about Mexico and Mexican immigrants. To back up his claim, he referenced a poll out of Nevada.

"I have a great successful building in Nevada," he said. "Tallest building in Nevada, anybody want a reservation? Let me know. But it's a great success. I employ many people. So when the press called today - they can't believe - they can believe I won Nevada in the poll. But they can't believe I won the Hispanic vote. I didn't win the Hispanic vote -- I won by a landslide. I said, I told you that. I keep telling you that. They love me, and I love them. I'm going to win the Hispanic vote. Bush isn't going to win, even though he'll say five words in Spanish."

Trump seemed to be referencing reports about a poll conducted by Gravis Marketing for One America News Network, which shows him leading the field of GOP contenders in Nevada -- and also shows him with a wide lead among Republican Hispanics. The poll seems to have relied on robocalling, which can be unreliable. Robocalls are particularly unreliable for polling Hispanic voters because the FCC prohibits robocalls made to cell phone numbers. In 2013, a CDC survey found Hispanic adults (49.9 percent) are more likely than non-Hispanic white (35.1 percent) or non-Hispanic black (39.4 percent) adults to be living in households with only wireless telephones.

Meanwhile, Univision on Thursday released the first national poll of Hispanic voters, and the results were not good for Trump. Conducted by the independent research firm Bendixen & Amandi International, the poll found that 71 percent of the Latino voters have a somewhat unfavorable or very unfavorable opinion of Donald Trump.

Among Republican Hispanics, Trump wins just seven percent support. By comparison, Jeb Bush won 38 percent, Marco Rubio won 22 percent and Ted Cruz won 12 percent.

In a match-up against Democrat Hillary Clinton among all Hispanic voters, 70 percent supported Clinton and 16 percent supported Trump.

Trump: ISIS is building a hotel

In addition to immigration, Trump has been very outspoken about the United States' fight against the Islamic State of Iraq and Syria (ISIS)

"ISIS is building a hotel - they're competing with me!" Trump declared at his Saturday rally, charging that the United States isn't doing enough to thwart the group.

There are indeed unconfirmed reports that ISIS has taken over the Ninawa International Hotel in Mosul, Iraq (though no reports that the group is building its own hotel).

Even so, ISIS isn't directly "competing" with Trump yet. The Trump Hotel Collection boasts properties around the world, including a hotel as far away as Azerbaijan, but it does not include hotels in Iraq or Syria.

Trump: Iraqis lost 2,300 Humvees the U.S. gave them

Trump on Saturday dismissed Iraqi leadership as corrupt thieves who let 2,300 Humvees disappear after "one bullet was fired in the air."

Indeed, Iraqi security forces lost 2,300 Humvees when ISIS took over Mosul, Iraqi Prime Minister Haider al-Abadi said on Iraqiya state TV.

While it's hyperbolic to refer to all of Iraq's leaders as corrupt thieves, U.S. military officials earlier this year did express frustration that Iraqi forces "just showed no will to fight" ISIS.

Trump's business relationships

"NBC wants me to do The Apprentice so badly. I said I can't, I'm going to run for president," Trump said Saturday. "So they renewed The Apprentice. I said I'm not going to do it. They didn't believe me."

NBC Universal did not respond to CBS News' request for comment on this, but the company did release a statement last month stating that it's cutting its business ties with Trump "due to the recent derogatory statements" he made regarding immigrants.

Backlash grows as Trump defends remarks on Mexican immigrants

The company said it is renewing "Celebrity Apprentice," which is licensed from Mark Burnett's United Artists Media Group. The New York Post reports that comedian George Lopez is in talks with NBC to take over the show.

Trump also gave his side of the story of his severed ties with Macy's. "I thought head of Macy's was a friend of mine," he said, recalling how he received a call from the executive who apologetically told Trump he's too "controversial."

Macy's told CBS News that it has no comment on Trump's remarks.

Trump also lambasted Univision, another company that's severed ties with him because of his controversial remarks about immigrants. "They're actually not wealthy at all," he said dismissively on Saturday. "They've got $10 billion in debt... I just sued Univision for $500 million."

Univision did, in fact, report $10.6 billion in outstanding debt in March, and Trump filed a lawsuit for breach of contract and defamation after Univision said it wouldn't air the Miss USA pageant.