Interestingly, I learned in detail how memory works in my psychology class. Through an experiment of memorization, it was found that the lesser intelligent classmates of mine had memorized less words in 10 seconds than the rest of the more intelligent people.

Do you think this would be to say that your ability to learn is based on your genes? I'm assuming that genes control this memorization ability, although other factors can hinder or help you.

Do you think that a person could achieve the same intelligence, but work harder, or is there lesser hope for them?

yes i fully agree this. genes helps lot to boost personality. it refers from one to another. genes are the thing that shows the complexion on people. like black people goes on giving birth to black child. and white gives birth to white baby.

genes help a lot but there is the intelligence with which you are born, this on one side, and the emotional intelligence on the other side.
The emotional intelligence deals with your motivation and dedication for learning something and is much very successful.