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.
II. 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


PS29502.01
Quantitative Review 2020 NEW QUESTION
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We know we have one person who takes no salt, and that person also takes no pepper. So either that one person takes *only* relish, or that person takes none of the three things.

But if that person takes *only* relish, then that is the person who takes no pepper. And the question tells us that the person who takes no pepper also takes no relish. So this person can't exist.

So the only possibility is that the person who takes no salt takes none of the three things. Then we only have 2 people left, and for 2 people to eat each of salt, pepper and relish, these 2 people must eat all three of the things. If we draw a 3-circle Venn diagram, we'll have a 2 right in the middle, where the three circles overlap, and we'll have 1 person who isn't in any circle at all.

Since that's our situation, we do have one person who eats none of the three things, so item I is true. And anyone who eats one thing eats everything, so II is true. And the person who takes no relish takes no salt, so III is true.
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Hi Archit,

Could you draw( i mean in your notebook and take picture) the Ven diagram of this and post here .
I am struggling to understand this .

I think the simplest way to solve this problem is to to make a table like the one below where P is the heading for the 'Persons' column and A, B and C denote the three persons. Let's imagine the table is blank and we have to fill in who takes what according the the information given. Let's start with "The one who takes no salt takes no pepper". Let's say B is that person so we put NO in the Pepper and Salt columns again'st B. Next, "The one who takes no pepper takes no relish". B is the only person who takes no pepper because both A and C must take pepper because it is stipulated that, "of the three persons, two take pepper" which means both A and C must take pepper. So we put NO against B in the Relish column. YES is an automatic choice for A and C in all the three food columns since it is given that "Of the three persons, two take relish, two take pepper and two take salt". Now let us proceed to the statements:

I. THE PERSON WHO TAKES NO SALT ALSO TAKES NO RELISH - B takes neither salt nor relish. So, TRUE.
II. ANY OF THE THREE PERSONS WHO TAKES PEPPER ALSO TAKES RELISH AND SALT - A and C take pepper and they both also take relish and salt. Also, TRUE.
III. THE PERSON WHO TAKES NO RELISH IS NOT ONE OF THE PERSONS WHO TAKE SALT - B is the person who takes no relish and he is not one of the person who takes salt. Again, TRUE.

Answer: E
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P RLS PPR SLT
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A YES YES YES
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B NO NO NO
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C YES YES YES
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This is written in a tricky way to make us assume that there has to be different people taking each one (at least that was my initial supposition) but the following sentence make this impossible: "The one who takes no salt takes no pepper, and the one who takes no pepper takes no relish."

If you draw a table you can see the relationship more clearly:



The only way to have 2 in each group and have the total add up to 6 is if 2 people take every condiment and the other takes none, i.e. the 3rd person is in the "neither" group in overlapping set formula.