It's natural to think of Meno's paradox but that paradox doesn't quite fit the bill :
A person cannot look for (zetein) what he knows or for what he
doesn't know. He would not look for what he knows, for he knows it
already and one who has the knowledge would have no need to look
for it. And he would not look for what he doesn't know, for then he
doesn't know what he is to look for (Plato, Meno 80e; Michael Welbourne, 'Meno's Paradox', Philosophy, Vol. 61, No. 236 (Apr., 1986), pp. 229-243 : 230).
I doubt if the remark you quote is attributable to anyone we're likely to discover, almost certainly not a philosophical 'name'. But if you're interested I'll try to assess the remark in its own right.
Roughly know the answer or know the rough answer ?
I'm not sure one can roughly know; one knows or one doesn't. I can, however, make perfect sense of knowing the rough (approximate or unspecific) answer. So I'll interpret the 'roughly know' in this way.
The epistemology of questions
There are clear cases where the questioner has no idea of what even a roughly correct answer is. If a child asks, 'Why is the sky blue ?', s/he almost certainly doesn't know anything about the physics of light - and doesn't the rough answer.
In other cases the questioner does know the rough answer but this is the very problem - they want and need a more precise answer. If I ask my partner, 'Where did we park the car ?', when we have been wandering happily through a foreign village and have lost our bearings. 'It's in the vicinity' is roughly correct, or even precisely true, but it's hardly the answer I want or need : what is precisely true is here not sufficiently specific. I know it's in the vicinity - we're in a village not a megalopolis. But just which street or square did we park the car in ? The 'rough answer', so unspecific, is in regard to what I want to know no answer at all.
In other cases, not only do I ask a question and not know the rough answer. There is no rough answer to know - there is a precise answer or nothing. Take this logical exercise from Lewis Carroll's Symbolic Logic. It is just false to say that when I first asked, 'What is the valid conclusion?', I already knew the rough answer or indeed that there is or was a 'rough' answer. There is and was one precise answer, nothing else :
All, who neither dance on tight ropes nor eat penny-buns, are old.
Pigs that are liable to giddiness are treated with respect.
A wise balloonist takes an umbrella with him.
No one ought to lunch in public who looks ridiculous and eats penny- buns.
Young creatures who go up in balloons are liable to giddiness.
Fat creatures who look ridiculous may lunch in public if they do not dance on tight-ropes.
No wise creatures dance on tight-ropes if they are liable to giddiness.
A pig looks ridiculous carrying an umbrella.
All, who do not dance on tight-ropes and who are treated with respect, are fat.
And the valid conclusion is ? I deduce that the valid conclusion is 'No wise young pigs are balloonists'. But to say that I already knew this answer when I first posed the question is cruel mockery !
- There are cases where from the nature, the specificity, of the question asked, the questioner probably does know the rough answer. If someone approaches me with a puzzled expression and asks : 'What are the three types of particle that atoms are made up of ?', it's likely (suppose we're in a science lab) that if the questioner knows enough about atoms to know that they are composed of three particles they probably do know that the answer is going to mention electrons, protons, and neutrons or something like that rather than plasma, lasers, and superfluids.