Of three persons, two take relish, two take pepper, and two take salt.

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

PS29502.01

IanStewart · Accepted Answer

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.

effatara · Answer

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
 _________________________________
 P RLS PPR SLT 
 _________________________________
 A YES YES YES 
 _________________________________
 B NO NO NO
 _________________________________
 C YES YES YES 
 _________________________________

energetics · Answer

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:

https://i.imgur.com/kZLsQYq.png

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.

Archit3110 · Answer

m1033512  solution attached

Posted from my mobile device

Archit3110 · Answer

we can solve by drawing a venn diagram

IMO E ; all three are correct.

m1033512 · Answer

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 .

manishcmu · Answer

When one who takes no salt takes no pepper, we can imagine fig A (pepper within salt). We just don't know whether pepper circle falls exactly over salt circle or whether pepper circle is inside salt circle.
Similarly, for pepper and relish.Since the question says - Of three persons, two take relish, two take pepper, and two take salt . All three circles must fall on each other exactly (fig B) with 2 people inside these three circles and 1 person outside all three circles. I, II, III are deducible from this.

ScottTargetTestPrep · Answer

Let’s say the 3 people are A, B and C and let’s say A takes no salt and pepper. Then B and C must take pepper and they also take salt. Furthermore, since the one who takes no pepper takes no relish, that person must be A since both B and C take pepper. In other words, A takes no condiments and B and C each take all 3 condiments. Therefore, all three statements are true.

Answer: E

Kinshook · Answer

R = Person taking relish
P = Person taking pepper
S = Person taking salt

IMO E

chrtpmdr · Answer

I usually solve questions with overlapping sets with a double matrix method.
Is there a equivalent to use (or a guide) when I have more then 2 options?

philippi · Answer

Yes, you can draw a diagram. If you scroll up you can see some people drawing a diagram with 3 overlapping sets.

GMATinsight · Answer

Please check the video explanation of the problem.

A good question to practice

Answer: Option E

https://www.youtube.com/watch?v=R41wT5o-bC0

sujoykrdatta · Answer

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.

#1. No salt => No pepper 
#2. No pepper => No relish

Thus it is obvious that: 
No salt => No pepper => No relish

But there are 2 (of the 3) who take salt, 2 take pepper and 2 take relish ... (i)

Thus, 1 person doesn't take salt, 1 doesn't take pepper and 1 doesn't take relish ... (ii)

But, no salt implies no pepper and that implies no relish

Thus, (ii) above refers to the same person who doesn't take any of the three things.

Conclusion: 
# One person doesn't take any of the three add-ons (salt, pepper, relish)
# Two people take all three add-ons (salt, pepper, relish)

Let's look at the statements:

I. The person who takes no salt also takes no relish - TRUE - he is the same person who takes no add-ons

II. Any of the three persons who takes pepper also takes relish and salt - TRUE - he is one of the 2 people who take all three add-ons

III. The person who takes no relish is not one of those who takes salt - TRUE - he is the one who takes no add-ons

Answer E

Posted from my mobile device

KarishmaB · Answer

3 people
6 instances (2 salt, 2 pepper, 2 relish)

The one who takes no salt takes no pepper, and the one who takes no pepper takes no relish.  - So say X takes no salt. Then X takes no pepper too. Then X takes no relish too! 
This means the other 2 people take all three things.

I. The person who takes no salt also takes no relish.
True. This person is X.

II. Any of the three persons who takes pepper also takes relish and salt.
True. These are the other two people.

II. The person who takes no relish is not one of those who takes salt.
X (one how takes no relish) is not one who takes salt. Correct. X does not take salt.

Answer (E)

Kinshook · Answer

Link to the solution posted on Youtube is provided below: - https://www.youtube.com/watch?v=sfuPXCC ... ZWYJ9-3dPe

WheatyPie · Answer

Just a small note Bunuel, the statements are improperly numbered.

Bunuel · Answer

_____________________
Fixed. Thank you.

Babineaux · Answer

Let three persons X, Y and Z

Now let X and Z are taking salt, Y is not taking salt so he is also not taking pepper.
Again Y is not pepper concludes he is not taking relish.

S______P______R
X______X______X
Z______Z______Z

Statement I: The person who takes no salt takes no relish which is Y, thus true.
Statement II: Any of three persons who takes pepper takes salt and relish, individually X and Z, thus true.
Statement III: The person who is taking no relish is not the one who is taking salt which is again Y, thus true.

Thus all of the statements are true.

IMO ans is E.

chacinluis · Answer

n=3
R=2 therefore R-complement=1
P=2 therefore P-complement=1
S=2 therefore S-complement=1

To say those that take no salt take no pepper means
S-complement is a subset of P-complement
and since S-complement and P-complement are of the same cardinality then 
S-complement=P-complement

To say those that take no pepper take no relish means
P-complement is a subset of R-complement
and since P-complement and R-complement are of the same cardinality then 
P-complement=R-complement

Therefore P-complement=S-complement=R-complement
Therefore P=S=R

Choice I. The person who takes no salt also takes no relish.
 True:  Since P-complement=R-complement

II. Any of the three persons who takes pepper also takes relish and salt.
 True:  Since P=S=R

III. The person who takes no relish is not one of those who takes salt. 
 True:  Since R-complement= S-complement. That is, the people who take no relish are the same people that don't take salt

Final Answer: E

Of three persons, two take relish, two take pepper, and two take salt.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Of three persons, two take relish, two take pepper, and two take salt.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards