And so the government has launched a campaign to convince parents that having daughters is a good thing: propaganda street banners preach that preferring boys over girls is old thinking; while school fees for girls have been reduced, and laws changed so daughters can inherit land.
And state-run TV programs show the government handing out cash to parents with only daughters. A pilot project rewards these parents from age 60 on with what amounts to $150 a year, a doubling of their yearly income.
Zhao says the cash handouts are not payoffs to have girls. "Not paying, but we call it incentive," she said, laughing.
But she told Stahl that even with all the incentives and the government programs, the gender imbalance is actually getting worse.
A lot of Americans and Europeans come to China to adopt Chinese babies, almost all girls. Asked whether, given the shortage of girls, the program is a good thing to continue, Zhao says: "I think it good for children themselves. But it is not good for a country to solve your problem."
For example, a hotel in Jiangxi province is filled year-round with families who come here to adopt. 60 Minutes saw people from Spain, the Netherlands, all over Europe, in the hotel.
This is a great irony: while China tries to increase its population of girls, they allow — albeit for humanitarian reasons — 12,000 to leave a year; 8,000 to the U.S. alone.
"Will China's sex imbalance, gender imbalance, ever get fixed as long as that one-child policy is in effect?" Stahl asked Valerie Hudson.
"I don't think that the Chinese government can really tackle the roots of this entrenched-son preference until it raises that ceiling on the number of children," she replied.
The ceiling has been raised for some rural families who can now have two or three children, but the government is unlikely to undo the one-child policy that it credits with reducing the population by 300 million people. That, they say, is the key to their rapid modernization.
Zhao says it's one of the reasons for the country's economic success. "If, today, we add another 300 million, can you imagine? So we think it's a great achievement."
So, in other words, another population explosion is more dreaded than the girl shortage.
Back at the No. 10 high school in Linchuan, students overwhelmingly told Stahl they want to have one child when they get married. Young people see small families as a patriotic duty.
"She'd like to ask if it's true that in America most families have one child," a female student asked Stahl through an interpreter.
"No, most families have two or three," Stahl explained.
This girl said she thinks Americans are "conceited" to have more than one child. In China, she said, "We're supporting the Motherland by having less."
Produced by Karen Sughrue