Which one of the following could be true?

Irina August 28, 2019

@sydneycrudo123,

Let's look at the setup for this game:

A pet shop features one of three breeds of kitten -H, M, S and one of three breeds of puppy - G, N, R on each day:

p

k
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7


(1) G are featured on day one

p G

k
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7

(2) No breed is featured on two consecutive days.

This rule tells us that day #2 cannot feature G.

(3) Any breed featured on day 1, cannot feature on day 7.

This rule tells us that day #7 cannot feature G.

p G N/R N/R

k
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7

(4) H are featured on exactly 3 days but not day 1.

Since H is not featured on day 1, and per rule (2) we cannot have H on two consecutive days, H must feature either on days 2, 4, and 6 or 3, 5, and 7.

p G N/R N/R

k M/S
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7

(5) R are not featured on day 7, nor on any day that features H.

Since G and R are not featured on day 7, we can conclude that N is featured on day 7.

p G N/R G/R N

k M/S
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7


Considering how restrictive the rule (4) is, we could sketch our a couple of scenarios for H in combination with the rest of the rules:

Scenario 1: H is on days 2,4, 6


p G N G/R G/N R/N G N

k M/S H M/S H M/S H M/S * opposite of #1
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7

Scenario 2: H is on days 3, 5, 7


p G R/N G/N G/N/R G/N G/R N

k M/S M/S* H M/S H M/S H
___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7

* opposite of #1

Now, the questions asks which one of the following could be true.

(A) There are exactly four breeds that are each featured on 3 days.

This answer choice tells us that there are only four breeds that are each featured on 3 days. We know that H are featured on exactly 3 days, the question is it possible that 3 more breeds are also featured on 3 days.

Let's look at the scenarios above. Per scenario 1, G could be featured on days 1, 3, and 6, N featured on days 2,4, 7, M featured on days 1, 3, 5, and H featured on days 2, 4, and 6. This could be true and (A) is thus the correct answer choice.

Even in the absence of these inferences in our initial setup, we could arrive to this answer choice by elimination. Let's look at the rest of the options:

(B) G are featured on every day that H are.

Let's look at our scenarios 1 and 2. Scenario 1, on day #2 N must be featured on the same day as H, so this is false. Scenario 2, N must be featured alongside H on day 7. Since it cannot be true in either scenario, this answer choice is incorrect.

(C) H are featured on every day that G are.

Incorrect. We know that G is #1, and H cannot be #1 per rule (4), hence it cannot be true.

(D) H are featured on every day that R are not.

Incorrect. We know that it cannot be true because day #1 is on of the days when G is featured and R is not, and H cannot be featured on day #1 per rule (4).

(E) R are featured on every day that H are not.

Incorrect. We know that H are not featured on day 1 per rule (4) and R are not featured on day 1 either per rule (1), hence this cannot be true.

Does this make sense?

Let me know if you have any further questions.