Imagine you asked someone about their plans and wishes for the future. Would it be correct to say:
What do you hope you'll have achieved by your thirty years old?
rather than:
What do you hope you'll have achieved by thirty?
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Sign up to join this communityThe grammatical reason you can't say
What do you hope you'll have achieved by your thirty years old?
is that your is a possessive adjective, so like any other adjective, it modifies nouns or noun phrases. This means it can only be followed by a noun or noun phrase, like your hat, your religion, your best suit. "thirty years old" isn't a noun or noun phrase, so you can't use it there. But you could say
What do you hope you'll have achieved by your thirtieth birthday?
because "thirtieth birthday" is a noun phrase.
"By thirty" or "by age thirty" is idiomatic. "By your thirty years old" is not. Some possibilities:
By (age) thirty what do you hope to achieve?
By the age of thirty, what do you hope to achieve?
When you reach thirty years old, what do you want to have achieved?
On your thirtieth birthday, what will you have wanted to achieve?