Logical Reasoning - Logical Problems - Discussion

Use Venn diagrams.

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.

(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.

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.

I agree you, thanks, @Ashwin Naik.

Thanks everyone for explaining.

The first statement is not a known fact.

All beverages are not drink mixes. So, all the red beverages might not be drink mixes.

Hence, we are not certain that some drink mixes are red. No drink mixes might be red if all the red beverages are not drink mixes.

I: Some drink mixes are red.Why it's not necessarily true: While some beverages are red, those red beverages do not have to overlap with the "drink mixes" category. They could be a completely different kind of beverage. So it's incorrect.

II: All beverages are drink mixes.Why it's not necessarily true: Fact 1 states all drink mixes are beverages, but the reverse is not always true (e.g., juice is a beverage, but it is not a drink mix). So, this statement is not correct.

III: All red drink mixes are drinkable.Why it must be true: By definition, a "red drink mix" is a drink mix. Since all drink mixes are beverages (Fact 1), and all beverages are drinkable (Fact 2), any drink mix—regardless of its color must be drinkable.

Answer should be option (E) - None of the statements is a known fact.

Explanation :

First you draw 3 concyclic circles, innermost for drink mix, middle one for beverages and outer for drinkable. Then one more circle intersecting outer two circles(Drinkable and Beverages) but not innermost circle(Drink mix) as the statement 3 says only some beverages(need not drink mix) are red. So some beverages surely including some drinkable may not include drink mix.

Its not necessary that some drink mixes are red. It might be the case that some drink mixes are red, but not necessarily. So, 1st statement is not true.

I will explain more: There are some beverages which are not drink mixes. So, it might be the case that all those beverages which are not drink mixes, are red. So, none of the drink mixes are red.