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

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Bunuel
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Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   26 Apr 2019, 06:17
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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


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E
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   26 Apr 2019, 07:30
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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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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   02 May 2019, 06:26
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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
_________________________________
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   28 Feb 2021, 05:51
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Video solution from Quant Reasoning starts at 9:36
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   30 Apr 2019, 09:02
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m1033512 solution attached

m1033512 wrote:
Archit3110 wrote:
we can solve by drawing a venn diagram

IMO E ; all three are correct.


Bunuel wrote:
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




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 .


Posted from my mobile device
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Archit3110
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   28 Apr 2019, 04:00
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we can solve by drawing a venn diagram

IMO E ; all three are correct.


Bunuel wrote:
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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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   30 Apr 2019, 07:01
Archit3110 wrote:
we can solve by drawing a venn diagram

IMO E ; all three are correct.


Bunuel wrote:
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




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 .
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   01 May 2019, 20:13
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.
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   23 May 2019, 17:18
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Bunuel wrote:
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


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
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   20 Jun 2019, 15:50
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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.
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   23 Aug 2019, 22:49
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Bunuel wrote:
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



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

IMO E
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   07 Oct 2019, 02:02
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?
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   27 Nov 2019, 08:15
chrtpmdr wrote:
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?


Yes, you can draw a diagram. If you scroll up you can see some people drawing a diagram with 3 overlapping sets.
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   14 Feb 2020, 01:53
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Bunuel wrote:
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


Please check the video explanation of the problem.

A good question to practice

Answer: Option E

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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   14 Feb 2020, 03:56
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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

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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   14 Feb 2020, 05:55
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Bunuel wrote:
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


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)
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   19 Apr 2020, 06:44
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Bunuel wrote:
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


Link to the solution posted on Youtube is provided below: -

https://www.youtube.com/watch?v=sfuPXCC ... ZWYJ9-3dPe
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   11 Jun 2020, 10:01
Just a small note Bunuel, the statements are improperly numbered.
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   11 Jun 2020, 10:26
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WheatyPie wrote:
Just a small note Bunuel, the statements are improperly numbered.


_____________________
Fixed. Thank you.
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink] New post   11 Jun 2020, 10:43
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.
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Re: Of three persons, two take relish, two take pepper, and two take salt. [#permalink]
11 Jun 2020, 10:43
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