Juarez's session CANNOT be on which one of the following days?

Irina on September 4, 2019

@ethan.thilavanh@gmail.com,

Let's look at the setup for this game:

Seven nurses - F G H J K L M - conduct seven sessions at a community center.

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

The following rules apply:

(1) At least two of the other nurses' sessions must fall in between H and M session.

H __ __ + M
M __ __ + H

(2)G session must be on the day before K

GK

This rule allows us to infer that K cannot be #1 and G cannot be #7

(3) J session must be on a later day than M
M > J

This rule allows us to infer than J cannot be #1 and M cannot be #7

___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7
~K ~M
~J ~G

(4) F session must be on an earlier day than K but on a later day than L

L > F > K

We can combine this rule with rule (2) to form the following chain:

L > F > GK
This rule tells us that K cannot be #1 or #2 or #3 because L F G must come before it, F cannot be #1 or #6 or #7, and L cannot be #5 or #6 or #7.

___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7
~K ~K ~K ~M
~J ~F ~F
~F ~G
~L ~L ~L

(5) L cannot conduct a session on the 2d.

___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7
~K ~K ~K ~M
~J ~F ~F
~F ~G
~L ~L ~L ~L

The question asks us which of the following days J CANNOT have a session on.

Let's look at the answer choices:

(A) 2d

If we put J second, we know that M has to be #1 per rule 3. L F G K chain could go in slots 3-6 and H in 7 as one of the possible options. This scenario works, hence (A) is incorrect.

M J L F G K H
1 2 3 4 5 6 7

(B) 3d

If we put J 3d, we could have M in slot #2, L in slot #1, and the rest of the nurses in the same positions. This scenario works as well, hence (B) is incorrect.

L M J F G K H
1 2 3 4 5 6 7

(C) 5th

If we put J 5th, we have no space for the L F G K sequence. Let's say LFGK are 1-4, this violates the second rule - M > J.

L F G K J
1 2 3 4 5 6 7

If GK are 6 and 7, the only way we could accommodate M __ __ + H rule is to have L in #2, which violates rule (5)

M L F H J G K
1 2 3 4 5 6 7

Since we cannot find an order that would comply with all the rules when J is #5, (C) is the correct answer.

(D) 6th

If we put J 6th, LF could be 1 &2, followed by M and G K in 3,4,5, and H in 7. Since this scenario complies with all the rules, (D) is incorrect.

L F M G K J H
1 2 3 4 5 6 7


(E) 7th

If J is 7th, we could simply switch H & J to maintain a valid order, hence (E) is incorrect.

L F M G K H J
1 2 3 4 5 6 7

Even though it might seem like a lot of work to try each of the answer choices, most of them required moving only one or two letters around to see that the sequence still complies with all the rules. (C) is the only option where we are unable to come up with a valid sequence and hence, J cannot be in spot #5.

Let me know if you have any further questions.