But first, let's meet the two youngsters.

Yvonne is 12, an only child. She and her parents share a rented three-bedroom flat in Mong Kok with their helper. Her father, David Cheung Ping-hang, manages a mini-storage facility in Cheung Sha Wan, and her mother is a housewife. Both hold university degrees: Cheung studied visual arts in Australia, and his wife is trained in architecture. The family own a property in another district, which they rent out.

Having completed primary education at the private Kowloon Tong School, Yvonne now attends Form One at Wa Ying College in Ho Man Tin. Unlike many parents, the Cheungs do not send her for tutoring, although her mother does sometimes help with her homework. She likes Roald Dahl's children's stories, enjoys science and fine art, and hopes to become an architect - a profession that would combine both of her loves.

"I like to go to school to learn. It's not about getting high marks. I believe learning can solve many problems in life," Yvonne says.

An active child, she's a member of Wa Ying's cross-country and basketball teams. Her weekends are taken up with piano and art classes, along with a public-speaking programme at the Brandon Learning Centre in Jordan. This is intended to bolster pupils' self-confidence, presentation skills and critical thinking, and be a useful preparation for studies abroad.

Cheung also hopes it will improve his daughter's English, though she doesn't seem to need help. Yvonne and the other three children in her class speak at near native levels.

At a recent session, the teacher leads a discussion about Henry Ford's ingenuity in devising mass production methods to make a car "for the multitudes". Yvonne and her three classmates are asked to fold paper planes as part of the exercise. Working individually and as a production line, the children wind up with about the same number of planes, but they learn the concept of manufacturing.

Afterwards, the students are given a few minutes to prepare, and then each gives a minute-long presentation on a different topic. Yvonne impresses everyone by launching into her presentation with an attention-grabbing question.

A rich cultural life is important to the Cheungs, so the couple have been taking Yvonne to galleries, museums and concerts since she was little. "My wife and I don't pressure her to earn a high salary or take up a certain job. We just want her to be happy," David Cheung says.

"Beyond her studies, we hope she will enjoy sports and learning outside textbooks because it will benefit her personal life, career and how she can contribute to society."

In nearby To Kwa Wan district, Angus has a very different life. He shares a cramped one-bedroom room flat in an old tenement building with his mother, Cao Caidi, and his younger sister. All three sleep in the same room.

They moved to Hong Kong from Jilong town in Guangdong province five years ago to join Angus' father, a Hongkonger, but his parents later separated.

The family do not receive any financial support from him, and they live on Cao's earnings as a part-time restaurant dishwasher and domestic helper. They do not have relatives in Hong Kong, so they return to Jilong every chance they get.

Although Angus spent a year in an adaptation programme for new immigrants, his poor English-language skills have made him an "overage" pupil. At 15, he's in Primary Six at Sheng Kung Hui Holy Carpenter Primary School in To Kwa Wan.

Over the past year, however, he has been getting help with his English homework at Principal Chan's Free Tutorial Centre, a non-profit service set up by former headmaster Chan Hung to help poor students who are losing out to wealthier children with access to tutoring.

Angus had just picked up the alphabet before he came to Hong Kong, so "you can imagine how much he had to catch up on'', says his tutor, retired teacher Cheng Yuet-sang. "He has come a long way to be reading English passages now. But where he needs the most work is learning new vocabulary."

The teenager also had to learn Cantonese in a hurry. In Jilong they spoke Putonghua and the Hakka dialect, so "I didn't have a choice but to start speaking Cantonese, so I just picked it up," he says. His Chinese, though, is "top-notch", Cheng says, recalling how his pupil had no trouble writing Chinese characters that Cheng had trouble with himself.

For other homework, Angus tries to complete them at school before it closes for the day at 5.30pm because a teacher familiar with the curriculum is assigned to help pupils with any questions. He loves taekwondo classes at school, particularly getting to spar with the other children at the end of the class, and likes reading Chinese sci-fi novels in his spare time. "I especially like stories that defy convention, with ideas that not a lot of people can think of."

Angus hasn't thought as far ahead as university or an ideal profession, but there is one thing he wants to achieve: he would love to build a computer game, he says.

Cao, his mother, is illiterate, and desperate for her two children to be well-educated; it's their only out if the family is to avoid being mired in poverty one generation after another.

"If my son does well in school, he can earn more and won't have to do backbreaking work like me," she says. "I always tell my son to work harder, but I can't help him with his homework. I feel helpless," she says.

Although she hopes he will go to university, Cao concedes: "I don't have high expectations, I just don't want him to work in the service sector or in delivery, because those jobs are so physically taxing."

The exposure and opportunities available to Yvonne and Angus are a study in contrasts. And if the HKIEd study is any indicator, these factors will probably set the two pupils on diverging paths - unless the government takes significant steps to ensure equal access to education.

Led by Professor Chou Kee-lee of the institute's Department of Asian and Policy Studies, the study examined the backgrounds of people at university entry age - 19- and 20-year-olds - in 1991 and 2011. Using census data, Chou and his team found that the university enrolment of young people from the richest 10 per cent of households in 2011 was 3.6 times higher than those from households with incomes of less than half of the median - 48.2 per cent from the wealthiest families were at university compared 13 per cent from families living in poverty. The gap is triple that from 20 years ago, when the difference was only 1.2 times (9.3 per cent enrolment for students from rich families and 8 per cent from poor families).

Moreover, chances of a young person securing a place in a degree programme are higher if he or she has a university-educated father, and lives in a family-owned residence.

The study found that 14 per cent of young people from single-parent household were enrolled in degree programmes in 2011 compared with 20.3 per cent of people who live with both parents. Also, just 3.2 per cent of new immigrant youth were enrolled in degree programmes in 2011 compared with 21.7 per cent of locally born youth.

Chou says the findings are alarming because although the number of university places has increased 60 per cent over the past 20 years to 16,600 in 2011, the opportunity seems increasingly out of reach to the less well-off.

In recent years, the need to help youngsters who are neither full-time students nor full-time workers - called "double have-nots" in Cantonese - has drawn increasing public attention. The study found that in 2011, about 19 per cent of youngsters living below the poverty line were in this category compared with 7.7 per cent of those from the wealthiest families in this category.

But those who are less well-off are still keen on getting a good education. In 2011, 30 per cent of young people in poverty were enrolled in post-secondary programmes, which includes certificate, higher diploma, associate degrees and sub-degree courses.

The figure was even higher than that for youngsters from the richest 10 per cent of households - 23.6 per cent. Two decades ago, the enrolment rates of the poorest and richest students in post-secondary programmes were equal, at approximately 16 per cent.

Yvonne and Angus both attend non-fee-paying schools. But as more popular aided schools are converting into fee-paying, direct-subsidy schools, poor families may be deterred from even applying, Chou says.

"This will create a class of 'noble' schools, hinder social upward mobility and worsen the disparity between rich and and poor," he says.

Chou calls for more scholarships or reduced-tuition schemes for deserving students, arguing that the government should devote more resources to schools with more students from poor households.