Hey can anyone help me in solving this GMAT question?

Question

Of three persons, two take relish, two take pepper, and two take salt. The one who takes no salt takes no pepper, and the one who takes no pepper takes no relish. Which of the following statements must be true? 
I. The person who takes no salt also takes no relish. 
II. Any of the three persons who takes pepper also takes relish and salt. III. The person who takes no relish is not one of those who takes salt.
 A. I only
 B. II only 
C. III only 
D. I and II only 
E. I, II, and III

Aarushi S · Accepted Answer

These logic puzzles are all about tracing the relationships carefully. The first thing to notice is the rule: the person who takes no salt also takes no pepper, and the one who takes no pepper also takes no relish. That means one person ends up taking none of the three items,  no salt, no pepper, and no relish.
Since only two people can take each item, and one person is out of all three, the other two must be the ones who take everything: relish, pepper, and salt.
So, Statement I is definitely true,  no salt means no relish for that person. Statement II is also true because the two who take pepper are also the ones who take all three. Statement III works too since the one with no relish is clearly not one of the people who took salt.
All three statements are true. Final answer is  E.

kritika K · Answer

This one&rsquo;s all about following the chain of exclusions logically.

Two people take salt,  one doesn&rsquo;t
The one who takes no salt also takes no pepper
That same person also takes no relish
So one person takes none of the three
The remaining two must take all three: relish, pepper, and salt
Statement I is true because no salt means no relish
Statement II is true because both pepper-takers also take salt and relish
Statement III is true because the person with no relish is the one who takes no salt

That confirms all three statements. Final answer is E . No need for a Venn diagram, just follow the logic chain step by step.