# 70% of the population drinks beer, 60% drinks vodka. What percent of the population drinks both?

Those are the only givens, no restriction as to what percentage of the population drinks neither beer nor vodka, but no given as to whether the whole population must drink either of the two.

I'm no mathematician, but in my lay opinion, I visualized this as a "slider" i.e.

BBBBBBB---
VVVVVV----


Where B is beer, '-' is nothing, and V is vodka. In the above configuration, 60% of the population drinks both. However, on the other extreme

---BBBBBBB
VVVVVV----


30% of the population drinks both.

Is it safe to say that 30-60% of the population drinks both beer and vodka?

(Friends have explained this to me in a Venn diagram, and they insist that 30% is the only correct answer. I understand that their Venn diagram looks exactly like my "other extreme" visualization, but why is it the only correct answer?).

Edit: It's also been argued that it can't be answered because of "not enough data", but I propose that it can be answered, just not discretely (IDK if that's the correct term, but I mean "definitely 30 or bust").

• You’re right; there might be people which drink neither. Nice visualization, btw. – Michael Hoppe Jan 16 '18 at 10:03
• In case you need to convince you're friends that $30\%$ isn't the only answer, it's hard to dispute the explicit example of a population of $10$ people, $6$ of whom drink both beer and vodka, and $1$ who drinks only beer. This set of people satisfies the criteria of the question: $70\%$ drink beer and $60\%$ drink vodka, while $60\%$ drink both. – preferred_anon Jan 16 '18 at 10:28
• @DanielLittlewood I like how "Explain Like I'm 5" this is. – lemuel Jan 16 '18 at 10:32
• It is probably assumed in the question that everyone drinks either beer or vodka. – Improve Jan 16 '18 at 10:34