Logical Reasoning - Logical Problems - Discussion

Answer should be C.

You are correct, I agree @Virendra.

According to me, it should be C.

Drink mixes = beverages.
Beverages = drinkable.
Some beverages = red.

I) some drink mixes are red:

Ok, we know that all drink mixes are beverages but it is not explained that all beverages are drink mixes so this answer is not a known fact.

II) All beverages are drink mixes:

It is the same explanation than upper. We know that all drink mixes are beverages but it is not explained that all beverages are drink mixes so this answer is not a known fact.

III) All red drink mixes are drinkable:

For this one, we need to make the deduction. Indeed, we know that all drink mixes are beverages and that some beverages are red so some drink mixes are red and as all beverages = drink mixes = drinkable Finally all red drink mixes are drinkable which is a known fact.

Let me clear the confusion for some:

"Choose your answer based solely on the information given in the FIRST THREE facts".

So just because the 3rd statement/question says "All red drink mixes are drinkable".

Doesn't make it a FACT from which you can base your decision.

The name drink mixes indicates that it is drinkable. So, all red drink mixes are drinkable. All drink mixes are beverages. Some beverages (drink mixers) are red. Both I and III are correct.

(I) All drink mixes are beverages.

Thus, some beverages may or may not be drink mixes.

(II) all beverages are drinkable.

Thus some drinkable may not be beverages. It again means all drink mixes are drinkable since all beverages are drinkable.

(III) some beverages are red.

Thus, some may not be read. It again means that the beverages that are red may either be drink or non-drink mixes thus all may be drink mixes or all may be non-drink mixes or mixture of drink and non-drink mixes.

Conclusion:

From the facts and analysis, we can say that all that part of beverages that are red can be drink mixes and if it is drink mixes then it is drinkable since all beverages are drinkable and all drink mixes are beverages. Therefore "All red drink mixes are drinkable" is a fact.

Moreover, since all red drink mixes is a fact, then "Some drink mixes is red" because if some were not red then how did they became drinkable in the fact we have already proven? Thus if some were not, then we wouldn't have all red drink mixes been drinkable.

Therefore option C is the answer.

Consider this example.

Drink mixes : Orange.

Beverages : Orange and Pomegranate.

Point 1:

All DM are B (so all orange are B).

Point 2:

All B are drinkable (so both orange and pomegranate are drinkable).

Point 3:

Some B are Red (so pomegranate are red).

Now Answer:

1. Some DM are Red = No in my example (can't say in general).

2. All B are DM = No, It say all DM are B nor B are DM.

3. All red DM are drinkable = Yes.

Use Venn diagrams.

Statement 1 is wrong because all drink mixes are beverages but all beverages are not drink mixes.

Beverages constitutes of drink mixes and non drink mixes. So coming to the statement 'some drink mixes are red' and we know SOME beverages are red.

These SOME may constitute of:

1. Complete drink mixes.
2. Complete non drink mixes.
3. Both drink mixes and non drink mixes.

So any of the combination is possible. So it may be true or may not be. That's why it is considered FALSE.

Hope you get it. Thank you.